Algebra 1 Common Core Student Edition, Grade 8-9

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