Fact o r i n g a Po l y n o m i a l M o d el
VX2 = TT • X • X
I h e GCF is x • x, or x2.
Step 3 Factor out the GCF.
4x2 - 7 tx 2 = x 2(4) + x2( -tt)
= x2(4 - ir)
The factored form of the area of th e sh ad ed region is x 2(4 — tt).Go t I t? 4. In Problem 4, suppose the side length of the square is 6x an d the radius of the
circle is 3x. W hat is the factored form of the area of th e shaded region?How can you find the
shaded region's area?
The shaded region is the
entire square except for
the circular portion. So,
subtract the area of the
circle from the area of
the square.
Helipads A helicopter landing pad, or helipad, is
sometimes marked with a circle inside a square so that
it is visible from the air. What is the area of the shaded
region of the helipad at the right? Write your answer in
factored form.
Step 1 Find the area of th e sh ad ed region.
A1 = s2 Area of a square
= (2x)2 S u b s titu te 2 x f o r s.
= 4x2 Simplify.
A2 = 7r r 2 A re a o f a c irc le
= ttx 2 Substitute x for r.
The area of the sh ad ed region is
A1 - A2, or 4x2 - ttx2.Step 2 Factor the expression.
First find the GCF.Lesso n Ch eck
Do yo u k n o w H OW?- W hat is a sim pler form of 6x(2x3 + 7x)?
- W hat is the GCF of th e term s in 4a4 + 6a 2?
Factor each polynomial.- 6 m2 — 15 m
- 4x3 + 8x2 + 12x
Do y o u UN DERSTAND? I f f l f PRANCES
Match each pair of monomials with its GCF.- 14«2, 35n4 A. 1
- 2In3,18«2 B. 7n2
- In2, 9 C. 3n2
8. R e a s o n i n g W rite a binom ial w ith 9x2 as th e GCF of
its term s.494 Chapter 8 Po l y n o m i al s an d Fact o r i n g