### About Factoring Polynomials using Substitution:

We previously mastered factoring a polynomial of the form ax^{2} + bx + c. In some cases, we will encounter a polynomial that is more complex but can be re-written through substitution. Once we perform the substitution, we factor as we normally do, then substitute one last time to obtain our final form.

Test Objectives

- Demonstrate the ability to factor out the GCF or -(GCF) from a group of terms
- Demonstrate the ability to re-write a polynomial using substitution
- Demonstrate the ability to factor a polynomial using substitution

#1:

Instructions: Factor each using substitution.

a) -2x^{6} - 7x^{3} + 15

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#2:

Instructions: Factor each using substitution.

a) 15x^{6} - 153x^{3} + 30

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#3:

Instructions: Factor each using substitution.

a) 10(x + 1)^{2} - 7(x + 1) + 1

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#4:

Instructions: Factor each using substitution.

a) 8x^{10} + 16x^{5} - 42

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#5:

Instructions: Factor each using substitution.

a) 15a^{8} + 42a^{4} + 24

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Written Solutions:

#1:

Solutions:

a) (-2x^{3} + 3)(x^{3} + 5)

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#2:

Solutions:

a) 3(5x^{3} - 1)(x^{3} - 10)

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#3:

Solutions:

a) (5x + 4)(2x + 1)

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#4:

Solutions:

a) 2(2x^{5} - 3)(2x^{5} + 7)

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#5:

Solutions:

a) 3(5a^{4} + 4)(a^{4} + 2)