Algebra 1
Name: _______________________________
Unit 6: Lesson 1-2
Date: _________________ Period: _______
Supplemental Wkst 2… Factoring Polynomials – Mixed Methods
(GCF and Grouping)
Section 1: Factor each polynomial using the “GCF” first. Write “prime” if the polynomial cannot be factored.
_________________ 1)
25x3  40 x 2  10 x
_________________ 2)
11d  88d 6
_________________ 3)
8a 4b4  28a3b3  4a 2b2
_________________ 4)
10c 2  3c
_________________ 5)
a 2b  ab2  c
_________________ 6)
16b4  4b3  8b2
Section 2: Factor each polynomial using “Grouping”. Write “prime” if the polynomial cannot be factored.
_________________ 7)
x3  3x  2 xy  6 y
_________________ 8) 6  2 y  3x 2  x 2 y
_________________ 9)
a( x  2)  2( x  2)
_________________ 10) 2ax  6 xc  ba  3bc
_________________ 11) 15k 3  35k 2  18k  42
_________________ 12) 3( x  y)  y( y  x)
Section 3: MIXED METHODS… Factor each polynomial. Write “prime” if it cannot be factored.
_________________ 13) 4h3  32h
_________________ 14) i(c  e)  y(c  e)
_________________ 15) 42mc  36md  7n2c  6n2 d
_________________ 16) 16n3  32n2  8n
_________________ 17) 6 y 4  9 y 3  27 y 2
_________________ 18)  8 p 3  24s 2 q
_________________ 19) 2 p3  16  m  32m2
_________________ 20)
6x  4
Section 4: Keystone Applications
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21 A)
21 B)
21 C)
21 D)
21 E)
Suppose you are building a model of the square castle shown below. The moat of the
model castle is made of colored paper. The castle is made by white paper.
A) Write a formula for the area of the entire model in terms of x.
B) Write a formula for the area of the castle in terms of x.
C) Write a formula in terms of x for the area A of the moat.
D) Factor your formula from part C .
E) Find A in square feet for x  30 feet
_________________ 22)
The formula for the surface area of a sphere is A  4  r 2 . A square sticker of side x is
placed on a ball of radius 3x . What is the surface area of the sphere not covered by the
sticker? Write your answer in factored form.