Math II ~ Mrs. Naylor
Handout 11-2: Multiplying and Factoring
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Simplify each product.
1) 7𝑥(𝑥 + 4)
2) 3𝑚2 (10 + 𝑚)
3) 4𝑥(2𝑥 3 − 7𝑥 2 + 𝑥)
Find the GCF of the terms of each polynomial.
4) 12𝑥 + 20
5) 45𝑏 + 27
6) 4𝑥 3 + 12𝑥 − 28
Factor each polynomial.
7) 9𝑥 − 6
9) 14𝑥 3 − 2𝑥 2 + 8𝑥
8) 14𝑛3 − 35𝑛2 + 28
10) A circular table is painted yellow with a red square in the middle. The
radius of the tabletop is 6x. The side length of the red square is 3x. What is
the area of the yellow part of the tabletop? Write your answer in factored
form.
Simplify. Write in standard form.
11) −2𝑥(5𝑥 2 − 4𝑥 + 13)
12) −5𝑦 2 (−3𝑦 3 + 8𝑦)
14) 𝑝(𝑝 + 2) − 3𝑝(𝑝 − 5)
15) 𝑡 2 (𝑡 + 1) − 𝑡(2𝑡 2 − 1)
13) 10𝑎(−6𝑎2 + 2𝑎 − 7)
16) 3𝑐(4𝑐 2 − 5) − 𝑐(9𝑐)
17) A rectangular wooden frame has side lengths 5𝑥 and 7𝑥 + 1. The rectangular opening for a
picture has side lengths 3𝑥 and 5𝑥. What is the area of the wooden part of the frame? Write your
answer in factored form. It might be helpful to draw a picture!
18) Describe and correct the error:
Factor each polynomial.
19) 17𝑥𝑦 4 + 51𝑥 2 𝑦 3
20) 9𝑚4 𝑛5 − 27𝑚2 𝑛3
21) 31𝑎6 𝑏 3 + 63𝑎5
22) Factor 𝑛2 + 𝑛. Suppose 𝑛 is an integer. Is 𝑛2 + 𝑛 always, sometimes or never an integer? Justify
your answer.