8th Grade Math

Polynomial Factoring

Learn how to factor quadratic expressions like x² + 7x + 12 into two binomials. Read the examples, work it out on the board, and type the factors in standard form below.

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$Professor Foxwell smiling$

How To Solve It

Factoring Steps

Use this pattern each time you generate a new problem.

1. Look at the last number

Find two numbers that multiply to make the constant term.

Example:

For x² + 7x + 12, the last number is 12.

Numbers that multiply to 12: 1 and 12, 2 and 6, 3 and 4.

2. Check the middle number

The same two numbers must also add up to the coefficient in front of x.

Example:

We need the sum to be 7.

3 + 4 = 7, so those are the numbers we want.

3. Write the factors

Put each number into its own parenthesis with x.

Example:

x² + 7x + 12 = (x + 3)(x + 4)

If the middle number is negative, the signs in the factors will be negative too.

4. Quick sign trick

Use the signs of the middle and last numbers to help.

If the last number is positive and the middle number is positive, both signs are +.
If the last number is positive and the middle number is negative, both signs are -.
If the last number is negative, one factor is + and one factor is -.

Current Problem Generate a factoring problem to begin.

Professor Foxwell will give you a quadratic expression to factor.

Helpful Math Words

Polynomial Factoring Vocabulary

Keep these words nearby while you practice.

Polynomial

An expression with one or more terms, like x² + 7x + 12.

Term

One part of an expression separated by plus or minus signs, like x², 7x, or 12.

Coefficient

The number attached to a variable. In 7x, the coefficient is 7.

Constant

A number without a variable. In x² + 7x + 12, the constant is 12.

Factor

A value or expression you multiply with another one. In (x + 3)(x + 4), each parenthesis is a factor.

Factoring

Rewriting a polynomial as a product of factors, such as turning x² + 7x + 12 into (x + 3)(x + 4).

Quadratic

A polynomial whose highest exponent is 2, like x² + 5x + 6.

Binomial

An expression with two terms, like x + 3 or x - 4.