About Factoring Polynomials using Substitution:
We previously mastered factoring a polynomial of the form ax2 + 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) -2x6 - 7x3 + 15
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#2:
Instructions: Factor each using substitution.
a) 15x6 - 153x3 + 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) 8x10 + 16x5 - 42
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#5:
Instructions: Factor each using substitution.
a) 15a8 + 42a4 + 24
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Written Solutions:
#1:
Solutions:
a) (-2x3 + 3)(x3 + 5)
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#2:
Solutions:
a) 3(5x3 - 1)(x3 - 10)
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#3:
Solutions:
a) (5x + 4)(2x + 1)
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#4:
Solutions:
a) 2(2x5 - 3)(2x5 + 7)
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#5:
Solutions:
a) 3(5a4 + 4)(a4 + 2)