^ Apply 0 36. Open-Ended Write a binom ial a n d a trinom ial using th e sam e variable. Divide the
trinom ial by the binom ial.- Think About a Plan The area A of a trapezoid is x3 + 2x2 — 2x — 3. The lengths of
its two bases b} and b 2 are x an d x2 - 3, respectively. W hat is an expression for the
height h of th e trapezoid? W rite your answ er in th e form q u o tien t + re^ ^ er.- W hat form ula can you use to find th e area of a trapezoid?
- How can you use the form ula to write an expression for hi
Divide.- (56a2 + 4a - 12) + (2a + 1)
- (3k3 - 0 .9 k 2 - 1.2k) -t- 3fc
- (64c3 - 125) -t- (5 - 4c)
- (2f 4 - 2 13 + 3t - 1) -h ( 2 13 + 1)
- (—2z3 - z + z2 + 1) -t- (z + 1)
39. (514 - 10t2 + 6) h- (t + 5) - (—7s + 6s2 + 5) -t- (2s + 3)
- (21 - 5r4 - 10r2 + 2 r6) (r2 - 3)
- (z4 + z2 - 2) - (z + 3)
- (6m3 + 3m + 70) h- (m + 4)
- Writing S uppose you divide a polynom ial by a binom ial. How do you know if the
binom ial is a factor of the polynom ial?
h- Geometry The volum e of the rectangular prism show n at the
right is m3 + 8m2 + 19m + 1 2. W hat is th e area of th e sh ad ed
base of the prism? - Look for a Pattern Find a p a ttern by dividing th e polynom ials. m + 3
a. W hat is [d 2 - d + 1) + (d + 1)?
b. W hat is (d 3 - d 2 + d - 1) -t- [d + 1)?
c. W hat is (d 4 — d 3 + d 2 — d + 1) (d + 1)?
d. W hat do you th in k w ould be the result of dividing
d 5 — d4 + d 3 — d 2 + d — 1 by d + 1?
e. Verify your prediction by dividing the polynom ials. - Business O ne way to m easu re a b u sin ess’s efficiency is by dividing the business's
revenue by its expenses. The an n u al revenue, in m illions of dollars, of a certain
airline can be m od eled by 200s3 - s 2 + 400s + 1500, w here s is th e n u m b e r of
passengers, in h u n d re d s of thousands. The expenses, in m illions of dollars, of the
airline can be m od eled by 200s + 300. W hat is the airline's revenue divided by its
expenses? Write your answ er in th e form q u o tien t 1 remainder - Reasoning If x + 3 is a factor of x2 - x •
divisor ‘
k, w h at is th e value of kl^225) 53. Physics C onsider th e form ula for distance traveled, d = rt.
a. Solve the form ula for t.
b. Use your answ er from p art (a). W hat is an expression for th e tim e it takes to
travel a distance of t 3 — 612 + 5 1 + 1 2 miles at a rate of t + 1 miles p e r hour?- Packaging Three tennis balls with radius r are packed into a cylindrical can w ith
radius r a n d height 6r + 1. W hat fraction of the can is empty? W rite your answ er in
th e form q u o tie n t+ ™ ^.
682 Chap t er 11 Rat io nal Expressions and Funct ions