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
Factoring using Substitution Test:
#1:
Instructions: Factor each using substitution.
a) -2x^{6} - 7x^{3} + 15
#2:
Instructions: Factor each using substitution.
a) 15x^{6} - 153x^{3} + 30
#3:
Instructions: Factor each using substitution.
a) 10(x + 1)^{2} - 7(x + 1) + 1
#4:
Instructions: Factor each using substitution.
a) 8x^{10} + 16x^{5} - 42
#5:
Instructions: Factor each using substitution.
a) 15a^{8} + 42a^{4} + 24
Written Solutions:
Solution:
a) (-2x^{3} + 3)(x^{3} + 5)
Solution:
a) 3(5x^{3} - 1)(x^{3} - 10)
Solution:
a) (5x + 4)(2x + 1)
Solution:
a) 2(2x^{5} - 3)(2x^{5} + 7)
Solution:
a) 3(5a^{4} + 4)(a^{4} + 2)