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
Factoring Polynomials using Substitution Practice Test:

#1:

Instructions: Factor each using substitution.

a) -2x6 - 7x3 + 15


#2:

Instructions: Factor each using substitution.

a) 15x6 - 153x3 + 30


#3:

Instructions: Factor each using substitution.

a) 10(x + 1)2 - 7(x + 1) + 1


#4:

Instructions: Factor each using substitution.

a) 8x10 + 16x5 - 42


#5:

Instructions: Factor each using substitution.

a) 15a8 + 42a4 + 24


Written Solutions:

#1:

Solutions:

a) (-2x3 + 3)(x3 + 5)


#2:

Solutions:

a) 3(5x3 - 1)(x3 - 10)


#3:

Solutions:

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


#4:

Solutions:

a) 2(2x5 - 3)(2x5 + 7)


#5:

Solutions:

a) 3(5a4 + 4)(a4 + 2)