1. In this lesson we will factor polynomials
To factor polynomials, we must first learn to divide monomials

2. Simplify the expression
Write the expression without exponents

3. Now cancel to simplify the expression4

4. Next, we will factor polynomials
What does each term in the polynomial have in common?
3x3 + 6x2 + 9x

5. Each term is divisible by 3 and x
We can ‘factor out’ the greatest common factor.
3x3 + 6x2 + 9x
3x(x2 + 2x + 3)

6. Factor out the greatest common factor in this polynomial
15x2 – 12x3
Each term contains the factor 3x2
3x2(5 – 4x)

7. The polynomial is modeled
x2 + 4x + 3
What are the factors?

8. Place x’s and 1’s on the top and left side to model the factors
x2 + 4x + 3 x x +1

9. Write the polynomial as the product of two binomialsx
x2 + 4x + 3 x +1
(x + 3)(x + 1)

10. Factor the polynomial
x2 + 6x + 9

11. Write as a product of binomials
x2 + 6x + 9
(x + 3)(x + 3) or (x + 3)2

12. Factor out the greatest common factor
-15x2 + 35x
Since the expression begins with a negative, factor out –5x
-5x(3x – 7)

13. We can also factor with a box
6x2 + 4x + 3x + 2
First, place the polynomial in a box
6x2 4x 3x 2

14. Next factor out the greatest common factor
6x2 + 4x + 3x + 2 3x 2x +1
6x2 4x 3x 2

15. Write the polynomial as the product of two binomials
6x2 + 4x + 3x + 2
(3x + 2)(2x + 1) 3x 2x +1
6x2 4x 3x 2

16. Complete Activity 9c Divide Monomials
Factor out the Greatest Common Factor
Factor Polynomials with Algebra tiles
Factor Polynomials with a box