NAME
DATE
5-6
PERIOD
Word Problem Practice
1. HEIGHT A ball tossed into the air
follows a parabolic trajectory. Its height
after t seconds is given by a polynomial
of degree two with leading coefficient
-16. Using synthetic substitution,
Norman found that the polynomial
evaluates to 0 for the values t = 0 and
t = 4. What is the polynomial that
describes the ball’s height as a function
of t?
4. EXPONENTIALS The exponential
function t = ex is a special function that
you will learn about later. It is not a
polynomial function. However, for small
values of x, the value of ex is very closely
approximated by the polynomial
function
1 3
1 2
x +−
x + x + 1.
e(x) = −
6
Use synthetic substitution to determine
e(0.1). Show your work.
-16t2 + 64t
2. SYNTHETIC SUBSTITUTION
Branford evaluates the polynomial
p(x) = x3 - 5x2 + 3x + 5 for a factor
using synthetic substitution. Some of his
work is shown below. Unfortunately, the
factor and the solution have ink spots
over it.
1
Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Companies, Inc.
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-5
11
6
0.1
5
759
Chapter 5
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62
1
−
2
1
−
60
31
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60
1
1
31
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631
−
v(x) = π(x3 - 5x2 - 86x + 360).
a. Use synthetic division to show that
x - 4 is a factor of v(x). Show your
work.
3. PROFIT The profits of Clyde’s
Corporation can be modeled by the
polynomial
P( y) = y4 - 4y3 + 2y2 + 10y - 200, where
y is the number of years after the
business was started. The chief financial
officer wants to know the value of P(10).
Use synthetic substitution to determine
P(10). Show your work.
-4
10
1
6
P(10) = 6100
6
one popular size of above-ground pool is
given by the polynomial
11; 764
1
1
−
600
6000
631
6631
1
−
−
−
6
600
6000
631
1−
6000
5. VOLUME The volume in cubic feet of
What is the factor he solved for? What
is the hidden solution?
10
2
See students' work.
b. Factor v(x) completely.
π(x - 4)(x + 9)(x - 10)
10 -200
620 6300
630 6100
c. What is the value of v(10)?
0
39
Glencoe Algebra 2
Lesson 5-6
The Remainder and Factor Theorems