Is th is p ro b le m
similar to one you've
seen before?
Yes. This p ro b le m is
similar to factoring a
trinom ial in one
variable o f th e fo rm
x2 + bx + c, where
c < 0.
Pr o b l em 4 Applying Factoring Trinomials
Geometry The area of a rectangle is given by the trinomial x2 — 2x - 35. What are
the possible dimensions of the rectangle? Use factoring.
.rKnQw .fr..T..ir r..
The area o f th e rectangle
Neec^^^
Possible d im ensions
of the rectangle
Ekn __________
Area = length x w id th , so fa c to r th e
trinom ial for area as the product of
binomials that represent the length
and w idth.
To fa cto r x2 - 2x - 35, identify th e p air of
factors of - 3 5 th a t has a sum of - 2.
x2 - 2x - 35 = (x + 5)(x - 7)
1 a n d - 3 5 -3 4
-1 and 35 34
5 a n d - 7 -2
-5 and 7 2
So the possible dim ensions of the rectangle are x + 5 and x — 7.
Go t I t? 4. A rectangle's area is x2 — x - 72. W hat are possible dim ensions of the
rectangle? Use factoring.
You can also factor som e trinom ials th a t have m ore th a n one variable. C onsider the
product (p + 9q\p + 7q).
(p + 9rjf)(p + 7 q) = p2 + 7pq + 9pq + 9q{7q)
= p 2 + I6pq + 63 q2
This suggests th at a trinom ial w ith two variables m ay be factorable if th e first term
includes th e square of one variable, the m iddle term includes b o th variables, a n d the
last term includes th e square of the o th er variable.
Pr o b l em 5 Fact o r i n g a Tr i n o m i al W i t h Tw o V a r i a b l e s
What is the factored form of x2 + 6 xy — 55y2?
List the pairs of factors of —55. Identify th e pair
that has a sum of 6.
x 2 + 6xy — 55y2 = (x — 5y)(x + lly )
sj Got It? 5. W hat is th e factored form of m2 + 6 mn — 27n2l
1 a n d - 5 5 -5 4
-1 and 55 54
5 and - 1 1 -6
-5 and 11 6
514 Chapter 8 Po l y n o m i al s an d Fact o r i n g