Page 559 - Algebra 1

Example
1
Factoring Perfect-Square Trinomials
Determine whether each polynomial is a perfect-square trinomial. If it is, factor the trinomial.
a. x2+6x+9 SOLUTION
x2 +6x+9
= x2 + 2 · 3x + 32 = (x + 3)2
b. x2-2x+4 SOLUTION
x2 -2x+4
≠ x2 - 2 · 1x + 22
c. 36x2 -48x+16 SOLUTION
36x2 - 48x + 16
= 4(9x2 - 12x + 4)
= 4[(3x)2 - 2 · (3x)(2) + 22] = 4(3x - 2)2
Write in perfect-square trinomial form. It is a perfect-square trinomial.
This is not equivalent to the perfect-square trinomial form. It is not a perfect-square trinomial.
Factor out 4.
Write in perfect-square trinomial form. It is a perfect-square trinomial.
Example
2
Application: Cell Phone Towers
A cellular phone tower’s signal covers a circular area
with a radius r in miles. The strength of the signal is
increased, and now covers an area of πr2 + 10πr + 25π r square miles. By how much did the radius of the coverage
area increase?
SOLUTION
Factor the expression for the new coverage area. πr2 + 10πr + 25π
= π(r2 + 10r + 25) Factor π out of the expression.
= π(r2 + 2 · 5r + 52) = π(r + 5)2 Write in perfect-square trinomial form.
The radius of the new circle is r + 5.
The radius of the coverage area increased by 5 miles.
Hint
The original area covered by the phone tower signal was πr2.
544 Saxon Algebra 1