About Factoring GCF:
Once we know how to find the greatest common factor (GCF) for a polynomial, the next step is to learn how to factor. We factor out the GCF by placing the GCF outside of a set of parentheses. Inside the parentheses, we divide each term by the GCF to get our new terms.
Test Objectives
- Demonstrate a general understanding of the meaning of the greatest common factor (GCF)
- Demonstrate the ability to find the greatest common factor (GCF) for a polynomial
- Demonstrate the ability to factor out the greatest common factor (GCF) for a polynomial
#1:
Instructions: Factor out the Greatest Common Factor (GCF).
a) $$-2x - 2$$
b) $$-20n^5 + 15n^3$$
Watch the Step by Step Video Solution View the Written Solution
#2:
Instructions: Factor out the Greatest Common Factor (GCF).
a) $$12n^2 - 9$$
b) $$64x^3y^2 + 8x^2y^2 + 16y^2$$
Watch the Step by Step Video Solution View the Written Solution
#3:
Instructions: Factor out the Greatest Common Factor (GCF).
a) $$-63x^5y - 21x^3y^2 + 28x^2$$
b) $$27x^5y^4 - 3xy + 9x$$
Watch the Step by Step Video Solution View the Written Solution
#4:
Instructions: Factor out the Greatest Common Factor (GCF).
a) $$72h^3j^2k^2 + 6h^3jk^2 - 54h^2jk^2 + 48h^2jk$$
Watch the Step by Step Video Solution View the Written Solution
#5:
Instructions: Factor out the Greatest Common Factor (GCF).
a) $$-121x^5zy + 33xz^3y + 77x^2z^2 + 22xz$$
Watch the Step by Step Video Solution View the Written Solution
Written Solutions:
#1:
Solutions:
a) $$2(-x - 1)$$
b) $$5n^3(-4n^2 + 3)$$
Watch the Step by Step Video Solution
#2:
Solutions:
a) $$3(4n^2 - 3)$$
b) $$8y^2(8x^3 + x^2 + 2)$$
Watch the Step by Step Video Solution
#3:
Solutions:
a) $$7x^2(-9x^3y - 3xy^2 + 4)$$
b) $$3x(9x^4y^4 - y + 3)$$
Watch the Step by Step Video Solution
#4:
Solutions:
a) $$6h^2jk(12hjk + hk - 9k + 8)$$
Watch the Step by Step Video Solution
#5:
Solutions:
a) $$11xz(-11x^4y + 3z^2y + 7xz + 2)$$
