### About Solving Polynomial Equations by Factoring:

In some cases, polynomial equations are solvable using factoring. Most often, we see problems that involve a quadratic equation. To solve this type of equation using factoring, we move all terms to the left side and write the resulting polynomial in standard form. The right side will simply be zero. At this point, we can factor the left side and set each factor with a variable equal to zero. Solving the resulting equations will give us our solution(s).

Test Objectives

- Demonstrate the ability to write a polynomial in standard form
- Demonstrate the ability to factor a polynomial
- Demonstrate the ability to use the zero product property to solve an equation

#1:

Instructions: Solve each equation using factoring.

a) 2p^{2} + 5p - 25 = 0

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#2:

Instructions: Solve each equation using factoring.

a) 7x^{2} + 33x + 20 = 0

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#3:

Instructions: Solve each equation using factoring.

a) 11x^{2} - 22x + 18 = -2 + 5x^{2}

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#4:

Instructions: Solve each equation using factoring.

a) 2a^{3} + a^{2} = 6a

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#5:

Instructions: Solve each equation using factoring.

a) x^{4} - 45x^{2} + 324 = 0

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Written Solutions:

#1:

Solutions:

a) p = -5 or p = 5/2

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#2:

Solutions:

a) x = -4 or x = -5/7

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#3:

Solutions:

a) x = 2 or x = 5/3

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#4:

Solutions:

a) a = 0 or a = -2 or a = 3/2

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#5:

Solutions:

a) x = 3 or x = -3 or x = 6 or x = -6