You can ad d polynom ials by adding like term s.Adding Polynomials
Travel A researcher studied the number of overnight stays in U.S. National Park
Service campgrounds and in the backcountry of the national park system over a
5-yr period. The researcher modeled the results, in thousands, with the following
polynomials.
Campgrounds: — 7.1x2 - 180x + 5800
Backcountry: 21x2 — 140x + 1900
In each polynomial, x = 0 corresponds to the first year in the 5-yr period. What
polynomial models the total number of overnight stays in both campgrounds and
backcountry?Know
- Overnight stays in campgrounds:
—7.1x 2 - 180* + 5800 - Overnight stays in backcountry:
21x 2 - 140x+ 1900
A p o ly n o m ia l fo r th e to ta l The w o rd both im plies
n u m b e r o f o v e rn ig h t addition, so add th e tw o
stays in campgrounds and
backcountrypolynom ials to fin d a
polynomial that represents
the total.Method 1 Add vertically.
Line u p like term s. Then ad d the coefficients.
—7.1x2 — 180x + 5800
+ 21x2 - 140x + 1900
13.9x2 - 320x + 7700Method 2 Add horizontally.
G roup like term s. Then ad d th e coefficients.
(~ 7 .1 x 2 - 180x + 5800) + (21x2 - 1 4 0x+ 1900)
= ( —7.1x2 + 21x2) + ( — 180x — 140x) + (5 8 0 0 + 1900)
= 13.9x2 - 320x + 7700A polynom ial th at m odels th e n u m b e r of stays (in th o u san d s) in cam pgrounds an d
backcountry over th e 5-yr p erio d is 13.9x2 — 320x + 7700.* Got It? 4. A n utritionist studied th e U.S. consu m p tio n of carrots an d celery a n d of
broccoli over a 6-yr period. The nutritionist m odeled the results, in m illions
of pounds, w ith the following polynom ials.
Carrots an d celery: - 1 2 x 3 + 106x2 — 241x + 4477
Broccoli: 14x2 - 1 4 x + 1545
In each polynom ial, x = 0 corresponds to th e first year in th e 6-yr period.
W hat polynom ial m odels th e total n u m b e r of pounds, in millions, of carrots,
celery, an d broccoli con su m ed in the U nited States during th e 6-yr period?488 Ch ap t er 8 Po l y n o m i al s an d Fact o r i n g