Operate On & Factor Polynomials

What you'll learn

Add, subtract, and multiply polynomials in one and two variables
Factor by grouping and factor trinomials
Factor special forms such as a difference of squares

Words to know

Polynomial —: a sum of terms with whole-number exponents
Term —: one part of a polynomial, like 5x^2
Trinomial —: a polynomial with three terms
Difference of squares —: a^2 - b^2 = (a - b)(a + b)
Factor by grouping —: group terms to reveal a common factor

Why it matters Factoring rewrites a polynomial as a product, which is the key step for simplifying expressions and solving equations.

Worked examples

Model ItI do

Factor x^2 + 5x + 6.

Find two numbers that multiply to 6 and add to 5: those are 2 and 3. So x^2 + 5x + 6 = (x + 2)(x + 3). The area model shows the four pieces x^2, 3x, 2x, and 6 adding back to the trinomial.

Try It TogetherWe do

Factor x^2 - 16.

This is a difference of squares: x^2 - 16 = x^2 - 4^2 = (x - 4)(x + 4).

Now YouYou do

Factor x^2 + 7x + 12.

Find two numbers that multiply to 12 and add to 7. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

1.Factor x^2 - 49.
2.Multiply (x + 3)(x + 4).
3.Factor 4x^2 + 8x.

On Level

The core Quick Check from the book.

1.Factor x^2 - 9.
2.Factor x^2 + 8x + 15.
3.Multiply (x + 2)(x + 5).
4.Factor 3x^2 + 6x.
5.Add (2x^2 + 3x) + (x^2 - x).

Challenge

Stretch your thinking.

1.Factor 6x^2 + 11x - 10.
2.Factor completely: x^3 - 4x^2 - 5x.
3.Factor by grouping: x^3 + 2x^2 - 9x - 18.