Algebra 1 Calculator

Q: What grade do you take Algebra 1 in?

Most students take Algebra 1 in 8th or 9th grade . Some schools offer it in 7th grade to students who finish pre-algebra early. There is no single rule. What matters is that you know how to work with fractions, negative numbers, and the order of operations before you start.

Q: What are like terms in algebra?

Like terms have the same variable with the same exponent . Only the number in front can be different. 3x and 7x are like terms. 5x² and 2x² are like terms. But 3x and 3x² are not , because the exponents differ. You can only add or subtract like terms: 3x + 7x = 10x.

Q: How do you know if a quadratic can be factored?

Find the discriminant, b² − 4ac. If it is a perfect square (like 0, 1, 4, 9, 16, 25), the quadratic factors with whole numbers. If it is not a perfect square, you need the quadratic formula or completing the square instead. Example: x² − 5x + 6 has 25 − 24 = 1, a perfect square, so it factors into (x − 2)(x − 3).

Q: What is the zero product property?

If two things multiply to zero, at least one of them must be zero . So if (x − 2)(x − 3) = 0, then either x − 2 = 0 or x − 3 = 0. That gives x = 2 or x = 3. This is why factoring solves equations. It only works when one side equals zero, so always move everything to one side first.

Q: How do you find the vertex of a parabola?

Use the formula x = −b ÷ (2a) to get the x-value. Then plug that number back into the equation to get the y-value. For y = x² − 6x + 5: x = 6 ÷ 2 = 3, and y = 9 − 18 + 5 = −4. The vertex is (3, −4). If a is positive the vertex is the lowest point. If a is negative it is the highest point.

Q: What is an extraneous solution?

An extraneous solution is an answer that looks correct but does not work in the original problem . It shows up when you clear fractions or square both sides. Example: in 1/(x − 3) = 5, if a step gives x = 3, you must throw it out, because it makes the denominator zero. Always plug answers back into the first equation.

Algebra 1 Calculator

Updated Sep 9, 2026 By Jehan Wadia

Introduction

This Algebra 1 calculator solves the math problems you see in class and shows every step. Type in a problem, press Calculate, and you get the answer along with the reasoning behind each move.

You can use it to:

Simplify or expand expressions
Evaluate an expression when x equals a number
Factor polynomials
Add, subtract, multiply, and divide polynomials
Simplify radicals and exponents
Solve equations, quadratics, and inequalities
Work with absolute value problems
Solve systems of two equations by substitution, elimination, or graphing
Find slope and the equation of a line from two points
Evaluate and compose functions

Each answer comes with a step-by-step solution that tells you why each move works, so you learn the rules instead of just copying a number. Many problems also show a graph, a table of values, or a number line so you can see what the answer means.

Not sure where to start? Pick a worked example from the drop-down menu. Already solved it on paper? Use the "Check My Work" box to see if your answer is right. Choose "Full Steps" when you are studying, or "Quick Answer" when you just need the result.

How to use our Algebra 1 Calculator

Pick what kind of math problem you want to do, type in your problem, and press Calculate. You get the answer, step-by-step work, a graph, a table of values, and a way to check your own answer.

Operation: Choose the type of problem from the drop-down list, like solve an equation, factor, simplify, or find slope. The input boxes change to match your choice.

Load a worked example: Pick a ready-made problem to fill in the boxes for you. This is a fast way to see how the calculator works.

Solution detail: Click "Full Steps" to see every step explained, or "Quick Answer" to see just the final answer.

Equation or expression box: Type your problem here using x as the variable. Use ^ for powers, / for fractions, and bars like |x| for absolute value.

Value of x: In Evaluate mode, type the number you want to plug in for x. Whole numbers, decimals, and fractions like 3/4 all work.

Solving method (quadratic): Choose quadratic formula, factoring, completing the square, or all three methods at once.

First and second polynomial: In Polynomial Operations mode, type one polynomial in each box, then pick add, subtract, multiply, or divide in the middle.

Equation 1 and Equation 2: For a system, type two equations that use x and y, then choose substitution, elimination, or graphing as your method.

Point 1 and Point 2: For lines, type the x and y numbers for each of your two points. The calculator finds the slope and the equation of the line.

Through point: Type an x and y for one more point. The tool uses it to build a parallel line and a perpendicular line.

f(x) and g(x): In Functions mode, type a rule for each function, then type the input value a to evaluate and compose them.

Root index, coefficient, and radicand: For radicals, pick the root (square, cube, and so on), type the number in front of the root, and type the one term that goes under the root.

Math keypad: Tap the buttons to add symbols like x, ^, √, |, ≤, and ≥ into the box you last clicked.

Window center and window width: Change these numbers to move and zoom the graph and the table of values.

Your answer: Type the answer you got on paper and press Check Answer to see if it matches.

What Is Algebra 1?

Algebra 1 is the math where letters stand for numbers. A letter like x is called a variable. It holds a number you do not know yet. The whole point of algebra is to find that number, or to write a rule that works for many numbers.

Expressions vs. Equations

An expression is a math phrase with no equal sign, like 3x + 5. You can simplify it or plug a number in for x, but you cannot "solve" it. An equation has an equal sign, like 3x + 5 = 20. It is a balance scale. Whatever you do to one side, you must do to the other side. That is how you get x by itself.

Solving Equations

To solve, you undo the math around x, step by step. Undo adding with subtracting. Undo multiplying with dividing. Work backward through the order of operations. When x is alone on one side, you have the answer. Always plug your answer back into the first equation to check it.

Inequalities

Inequalities use <, >, ≤, or ≥ instead of an equal sign. They have many answers, not just one. You solve them almost the same way as equations, with one big rule: if you multiply or divide both sides by a negative number, flip the sign. Answers are shown on a number line. A filled dot means the number is included. An open dot means it is not.

Factoring and Quadratics

A quadratic has an x² term, like x² − 5x + 6 = 0. Its graph is a U-shaped curve called a parabola. There are three main ways to solve one: factoring, completing the square, and the quadratic formula. Factoring means writing the polynomial as things multiplied together, like (x − 2)(x − 3). Then you set each part equal to zero. The discriminant (b² − 4ac) tells you how many real answers to expect: positive means two, zero means one, negative means none.

Lines and Slope

Slope is how steep a line is. It equals rise over run, or (y₂ − y₁) ÷ (x₂ − x₁). The form y = mx + b shows the slope (m) and the y-intercept (b), the spot where the line crosses the y-axis. Parallel lines have the same slope. Perpendicular lines have slopes that are opposite reciprocals, so their product is −1.

Systems of Equations

A system is two equations at once. The answer is the point (x, y) that makes both true. On a graph, that is where the two lines cross. You can solve by substitution, by elimination, or by graphing. If the lines are parallel, there is no answer. If they are the same line, there are endless answers.

Functions and Radicals

A function is a rule: put one number in, get exactly one number out. We write it as f(x). The domain is every input allowed. The range is every output you can get. Radicals are roots, like √50. To simplify a radical, pull out perfect square factors: √50 = √(25 · 2) = 5√2.

Why Algebra 1 Matters

Algebra 1 is the base for geometry, Algebra 2, and every math class after that. It also shows up in real life: figuring out cost per item, comparing phone plans, mixing recipes, and reading charts. Learning the steps now makes later math much easier.

Formulas used

Quadratic formula

x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}

Discriminant of a quadratic

\Delta = b^2 - 4ac

Vertex of a parabola

x = \frac{-b}{2a},\qquad y = f\!\left(\frac{-b}{2a}\right)

Completing the square

x^2 + \frac{b}{a}x + \left(\frac{b}{2a}\right)^2 = -\frac{c}{a} + \left(\frac{b}{2a}\right)^2 \;\Longrightarrow\; \left(x + \frac{b}{2a}\right)^2 = \frac{b^2 - 4ac}{4a^2}

Slope between two points and line equations

m = \frac{y_2 - y_1}{x_2 - x_1},\qquad y - y_1 = m(x - x_1),\qquad y = mx + b

Parallel and perpendicular slopes

m_{\parallel} = m,\qquad m_{\perp} = -\frac{1}{m}

Solution of a 2x2 linear system (Cramer's rule)

x = \frac{c_1 b_2 - c_2 b_1}{a_1 b_2 - a_2 b_1},\qquad y = \frac{a_1 c_2 - a_2 c_1}{a_1 b_2 - a_2 b_1}

Absolute value equation and inequality cases

|u| = k \Rightarrow u = \pm k,\qquad |u| \le k \Rightarrow -k \le u \le k,\qquad |u| \ge k \Rightarrow u \le -k \ \text{or}\ u \ge k

Frequently asked questions

What grade do you take Algebra 1 in?

Most students take Algebra 1 in 8th or 9th grade. Some schools offer it in 7th grade to students who finish pre-algebra early. There is no single rule. What matters is that you know how to work with fractions, negative numbers, and the order of operations before you start.

What is the difference between Algebra 1 and Algebra 2?

Algebra 1 teaches the basics: variables, linear equations, inequalities, slope, factoring, and simple quadratics.

Algebra 2 builds on that with harder topics like complex numbers, logarithms, exponential functions, polynomials of higher degree, and conic sections. Geometry usually comes between the two.

What does PEMDAS mean?

PEMDAS is the order you do math operations:

P for Parentheses
E for Exponents
M/D for Multiply and Divide, left to right
A/S for Add and Subtract, left to right

Multiply and divide are equal in rank, so you go left to right. Same for add and subtract. Example: 3 + 4 × 2 = 3 + 8 = 11, not 14.

What are like terms in algebra?

Like terms have the same variable with the same exponent. Only the number in front can be different.

3x and 7x are like terms. 5x² and 2x² are like terms. But 3x and 3x² are not, because the exponents differ. You can only add or subtract like terms: 3x + 7x = 10x.

Why do you flip the inequality sign when you divide by a negative number?

Because multiplying by a negative flips the number line around.

Start with a true statement: 2 < 6. Multiply both sides by −1 and you get −2 and −6. But −2 is bigger than −6, so the sign must flip: −2 > −6. The same thing happens in any inequality, so flip the sign every time you multiply or divide both sides by a negative.

What does FOIL mean in algebra?

FOIL is a trick for multiplying two binomials like (x + 3)(x + 5). It stands for First, Outer, Inner, Last.

First: x · x = x²
Outer: x · 5 = 5x
Inner: 3 · x = 3x
Last: 3 · 5 = 15

Add them up and combine like terms: x² + 8x + 15. FOIL only works for two terms times two terms. For bigger ones, distribute every term.

How do you know if a quadratic can be factored?

Find the discriminant, b² − 4ac. If it is a perfect square (like 0, 1, 4, 9, 16, 25), the quadratic factors with whole numbers. If it is not a perfect square, you need the quadratic formula or completing the square instead.

Example: x² − 5x + 6 has 25 − 24 = 1, a perfect square, so it factors into (x − 2)(x − 3).

What is the zero product property?

If two things multiply to zero, at least one of them must be zero.

So if (x − 2)(x − 3) = 0, then either x − 2 = 0 or x − 3 = 0. That gives x = 2 or x = 3. This is why factoring solves equations. It only works when one side equals zero, so always move everything to one side first.

How do you find the vertex of a parabola?

Use the formula x = −b ÷ (2a) to get the x-value. Then plug that number back into the equation to get the y-value.

For y = x² − 6x + 5: x = 6 ÷ 2 = 3, and y = 9 − 18 + 5 = −4. The vertex is (3, −4). If a is positive the vertex is the lowest point. If a is negative it is the highest point.

What is an extraneous solution?

An extraneous solution is an answer that looks correct but does not work in the original problem. It shows up when you clear fractions or square both sides.

Example: in 1/(x − 3) = 5, if a step gives x = 3, you must throw it out, because it makes the denominator zero. Always plug answers back into the first equation.

What is the difference between AND and OR compound inequalities?

AND means both parts must be true at the same time. The answer is one interval between two numbers, like −3 < x < 5.

OR means only one part needs to be true. The answer is two separate pieces going in opposite directions, like x < −3 or x > 5. Absolute value gives AND for < problems and OR for > problems.

How do you write an answer in interval notation?

Write the smallest number, a comma, then the largest number.

Use ( ) when the endpoint is not included (< or >).
Use [ ] when it is included (≤ or ≥).
Always use ( ) next to ∞ or −∞.

So x ≥ 2 becomes [2, ∞), and −1 < x ≤ 4 becomes (−1, 4]. Two separate pieces are joined with ∪.

How do you divide polynomials with long division?

It works like number long division. Repeat these four steps:

Divide the first term of the dividend by the first term of the divisor.
Multiply that answer by the whole divisor.
Subtract the result, and watch the signs.
Bring down the next term and repeat.

Stop when the leftover has a lower degree than the divisor. That leftover is the remainder.

What is the GCF and how do you factor it out?

GCF stands for greatest common factor, the biggest thing every term shares. Look at the numbers and the variables.

In 6x³ − 12x², the numbers share 6 and the variables share x², so the GCF is 6x². Pull it out front: 6x²(x − 2). Factoring the GCF first always makes the rest of the problem easier.

Why does an absolute value equation have two answers?

Absolute value means distance from zero, and distance can go two ways. Both 7 and −7 sit 7 units from zero, so |x| = 7 gives x = 7 and x = −7.

For |2x − 3| = 7, set the inside equal to 7 and to −7, then solve both. If an isolated absolute value equals a negative number, there is no solution, since distance is never negative.

What does a fractional exponent like x^(1/2) mean?

A fractional exponent is another way to write a root. The bottom number is the root and the top number is the power.

x^(1/2) = √x
x^(1/3) = ∛x
x^(2/3) = ∛(x²)

So 8^(1/3) = 2, and 8^(2/3) = 4. Both forms mean the same thing, so use whichever is easier.

How do you tell if an equation has no solution or infinitely many solutions?

Simplify both sides. If the variable disappears, look at what is left.

A false statement like 1 = −3 means no solution.
A true statement like 6 = 6 means infinitely many solutions, and every number works.

If the variable stays, you get one normal answer.

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