# Polynomial factoring

I need some help with these problems. Please see attachment.

Please show all work to each equation

Factor out the GCF in each expression

1) 15x^2y^2 - 9xy^2 + 6x^2y

2) a(a + 1) -3(a + 1)

Factor each polynomial completely

3) x^3y + 2x^2y^2 + xy^3

Use grouping to factor each polynomial completely

4) x^3 + ax + 3a + 3x^2

Factor each polynomial. If the polynomial is prime, say so.

5) 18z + 45 + z^2

Factor each polynomial completely. Use the methods in the previous examples. If the polynomial is prime say so.

6) 3x^2y^2 - 3x^2y^2 + 3xy^2

Factor each trinomial using the ac method.

Strategy for factoring ax^2 + bx + c by the ac Method

To factor the trinomial ax^2 + bx + c:

1. Find two numbers that have a product equal to ac and a sum equal to b.

2. Replace bx by two terms using the two new numbers as coefficients.

3. Factor the resulting four-term polynomial by grouping

7) 2x^2 + 11x + 5

Factor each polynomial completely.

8) a^2b + 2ab - 15b

Factor each polynomial completely. If a polynomial is prime, say so.

9) 3x^2 - 8x - 5

10) 3x^2 - 18x - 48

11) 9x^2 + 4y^2

Solve by factoring. Use the strategy for solving equations by factoring section below.

Strategy for Solving an Equation by Factoring

1. Rewrite the equation with 0 on one side.

2. Factor the other side completely.

3. Use the zero factor property to get simple linear equations.

4. Solve the linear equations.

5. Check the answer in the original equation.

6. State the solution(s) to the original equation.

The Zero Factor Property

The equation a * b = 0 is equivalent to

a = 0 or b = 0.

12) 2h^2 - h - 3 = 0

Solve the equation

13) 12m^3 - 13m^2 + 3m = 0

14) m^2 + 8/3m = 1

#### Solution Summary

This provides several examples of factoring polynomials, as well as of solving polynomial equations.