Virginia SOL Math / Algebra I / Expressions & Operations

A.EO.2

Operations & Factoring Polynomials

What you'll learn

  • Add, subtract, and multiply polynomials in one variable
  • Factor out the greatest common factor of a polynomial
  • Factor trinomials of the form x^2 + bx + c

Words to know

Polynomial —
a sum of terms with whole-number exponents
Monomial —
a polynomial with one term, like 4x
Binomial —
a polynomial with two terms, like x + 3
Trinomial —
a polynomial with three terms, like x^2 + 5x + 6
Factor —
write a polynomial as a product of simpler polynomials
GCF —
the greatest common factor shared by all terms

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

Worked examples

Model ItI do

Factor x^2 + 5x + 6.

Find two numbers that multiply to 6 and add to 5: 2 and 3. So x^2 + 5x + 6 = (x + 2)(x + 3), which the area model confirms.

Try It TogetherWe do

Multiply (x + 4)(x + 2).

Use FOIL: x*x + x*2 + 4*x + 4*2 = x^2 + 2x + 4x + 8. Combine like terms: x^2 + 6x + 8.

Now YouYou do

Factor 6x^2 + 9x by pulling out the GCF.

Find the greatest common factor of both terms, then divide it out. Check your answer in the back of this chapter.

Practice

Mastered 0 of 11

Warm-up

Ease in with the basics.

  1. 1.Add: (x^2 + 2x) + (3x^2 + x).

  2. 2.Factor out the GCF: 3x + 6.

  3. 3.Subtract: (7x + 4) - (2x + 1).

On Level

The core Quick Check from the book.

  1. 1.Add: (2x^2 + 3x) + (x^2 - 5x).

  2. 2.Multiply: (x + 3)(x + 5).

  3. 3.Factor: x^2 + 7x + 12.

  4. 4.Factor out the GCF: 4x^2 + 8x.

  5. 5.Subtract: (5x - 2) - (2x + 3).

Challenge

Stretch your thinking.

  1. 1.Multiply: (x - 3)(x + 4).

  2. 2.Factor: x^2 - 5x + 6.

  3. 3.Factor completely: 2x^2 + 10x + 12.