Mixed Review Of Factoring Worksheet

ADVERTISEMENT

Mixed Review of Factoring
Start at the top of the flow chart and work your way down the chart:
1.
Factor out the G.C.F. (top of the flow chart).
2.
Determine whether the polynomial has two, three, or four or more
terms.
3.
If the polynomial has four or more terms, factor by grouping (left
side of the chart).
4.
If the polynomial has three terms, first check to see if it is a perfect
square trinomial. If not, then factor it either using the trial-and-error
method or the AC-method (middle part of the chart).
5.
If the polynomial has two terms, first check to see if it is a difference
of squares (remember the sum of squares is prime). If not, check to
see if it is a sum or difference of cubes (right side of the chart).
6.
Always check to see if everything is completely factored (bottom of
the flow chart). If not, go through the flow chart again.
Examples:
3
2
2
3
a)
64x
y + 112x
y
– 32xy
1.
The G.C.F. is 16xy. Factoring out 16xy, we get:
3
2
2
3
64x
y + 112x
y
– 32xy
2
2
= 16xy(4x
+ 7xy – 2y
)
2.
The polynomial inside the parentheses has 3 terms.
2
4.
Since – 2y
is not a perfect square, then the trinomial is not a
perfect square trinomial. We will factor it using trial-and-error:
2
2
16xy(4x
+ 7xy – 2y
)
x • 4x
– y • 2y
16xy(x – y)(4x + 2y)
2x • 2x
No, G.C.F. ≠ 1
16xy(2x – y)(2x + 2y)
16xy(x + 2y)(4x – y)
No, G.C.F. ≠ 1
O.
– xy
I.
8xy
7xy Yes
6.
Everything is factored, so the answer is 16xy(x + 2y)(4x – y).
2
2
b)
54m
– 24z
1.
The G.C.F. is 6. Factoring out 6, we get:
2
2
54m
– 24z
2
2
= 6(9m
– 4z
)
2.
The polynomial inside the parentheses has 2 terms.

ADVERTISEMENT

00 votes

Related Articles

Related forms

Related Categories

Parent category: Education
Go
Page of 3