IM3 – UNIT 1: FACTORING REVIEW
Factoring Polynomials Using a GCF - Factoring polynomials is an important algebra skill. One
common method is factoring out the Greatest Common Factor (GCF). The GCF is the largest
expression that divides each term of the polynomial without leaving a remainder. When you
factor out the GCF, you rewrite the polynomial as the product of the GCF and another
polynomial. This makes more complicated factoring and solving easier!
Fill in the Blank: Fill in the blank with the correct words.
1. The first step in factoring a polynomial using a GCF is to identify the _______ that is
common to all terms.
2. When factoring 6x3 + 9x2 the GCF is: ______________
3. Factoring 8y4 - 12y2 by the GCF gives: 4y2 (__________________)
4. If a polynomial has no common factor other than 1, it is called ____________ in terms of
factoring by GCF.
5. Factoring 15a2b - 10ab2 -- what is the GCF? ___________.
Word bank: 3x2 GCF prime
4y2
(2y2 - 3)
5ab
6. Factor 18x4y2 - 24x2y3 by its GCF and show your steps.
= __________ (
)
Multiple Choice Questions: Choose the correct answer from the choices for each question.
1. What is the GCF of 12x2y and 18xy2?
o a) 6xy
o b) 3x2y2
o c) 2x
o d) 12y
2. Which of the following is 21m3n - 14m2n2 factored by its GCF?
2
o a) 7m n(3m - 2n)
3
2
o b) 7n(m - 2m n)
3 2
o c) 7m n (3 - 2)
2
o d) 14mn(1.5m - n)
3. What is the GCF of 5a2b, 10ab2, and 15ab?
o a) 5ab
2
o b) 15ab
o c) 10ab
2 2
o d) a b
4. Which shows 4x2 - 8x factored by the GCF?
o a) 4x(x-2)
2
o b) 2(x -4x)
o c) 4(x-2x)
2
o d) 8(x -x)
5. If the GCF of a polynomial is 1, what does that mean?
o a) The terms have no common factor except 1.
o b) The polynomial can be factored further.
o c) The GCF is always the constant term.
o d) The polynomial is zero.
Open-Ended Question: Answer the following questions in complete
sentences.
6. Explain, in your own words, why it is helpful to factor a
polynomial by its GCF before attempting other factoring methods.