3
2
p (x) = ± x + 3x ± 5
5-3 Polynomial Functions
CCSS PERSEVERANCE State the degree and
leading coefficient of each polynomial in one
variable. If it is not a polynomial in one variable,
explain why.
6
5
±6x ± 4x + 13xy
6
8x ± 12x + 14x ± 9
$16:(5
degree = 6, leading coefficient =±12
2
15x ± 4x + 3x ± 5x
4
$16:(5
degree = 4, leading coefficient = ±5
(d + 5)(3d ± 4)
$16:(5
degree = 2, leading coefficient = 3
5
4
9
6x ± 5x + 2x ± 3x
$16:(5
18a ± 12a + 3
2
c(b )
$16:(5
3
3
If c(x ) = 2x 2 ± 4 x + 3 and d (x ) =± x 3 + x + 1, find
each value.
c(3a )
2
$16:(5
not in one variable because there are two variables, x
and y .
5
$16:(5
p (±6) = 319; p (3) = ±5
4
2
2b ± 4b + 3
d (4y ± 3)
$16:(5
3
2
±64y + 144y ± 104y + 25
For each graph,
a. describe the end behavior,
b. determine whether it represents an odddegree or an even-degree function, and
c. state the number of real zeros.
2
$16:(5
degree = 9, leading coefficient = 2
Find p (±6) and p (3) for each function.
4
2
p (x) = x ± 2x + 3
$16:(5
p (±6) = 1227; p (3) = 66
3
2
p (x) = 2x + 6x ± 10x
$16:(5
p (±6) = ±156; p (3) = 78
3
$16:(5
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at four points, so
there are four real zeros.
2
p (x) = ± x + 3x ± 5
$16:(5
p (±6) = 319; p (3) = ±5
If c(x ) = 2x 2 ± 4 x + 3 and d (x ) =± x 3 + x + 1, find
each value.
c(3a )
$16:(5
2
18a ± 12a + 3
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2
c(b )
$16:(5
a.
b. Since the end behavior is in opposite directions, it
is an odd-degree function.
c. The graph intersects the x-axis at one point, soPage 1
there is one real zero.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at four points, so
5-3 Polynomial
Functions
there are four
real zeros.
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at no points, so
there are no real zeros.
$16:(5
a.
b. Since the end behavior is in opposite directions, it
is an odd-degree function.
c. The graph intersects the x-axis at one point, so
there is one real zero.
$16:(5
a.
b. Since the end behavior is in opposite directions, it
is an odd-degree function.
c. The graph intersects the x-axis at one point, so
there is one real zero.
$16:(5
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at two points, so
there are two real zeros.
$16:(5
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at two points, so
there are two real zeros.
Find p (±2) and p (8) for each function.
$16:(5
p (±2) = ± 0.5; p (8) = 3112
$16:(5
a.
b. Since the end behavior is in the same direction, it
is an even-degree function.
c. The graph intersects the x-axis at no points, so
there are no real zeros.
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$16:(5
p (±2) = 1.5; p (8) = 304
Use the degree and end behavior to match each
polynomial to its graph.
A.
Page 2
2
f (x) = ± 2x + 8x + 5
$16:(5Functions
5-3 Polynomial
p (±2) = 1.5; p (8) = 304
Use the degree and end behavior to match each
polynomial to its graph.
A.
$16:(5
B
4
2
f (x) = x ± 3x + 6x
$16:(5
A
3
2
f (x) = ± 4x ± 4x + 8
$16:(5
C
3
2
If c(x ) = x ± 2 x and d (x ) = 4x ± 6 x + 8, find
each value.
3c(a ± 4) + 3d (a + 5)
B.
$16:(5
3
2
3a ± 24a +240a + 66
2
± 2d (2a + 3) ± 4c(a + 1)
$16:(5
C.
D.
3
2
f ( x ) = x + 3x ± 4x
$16:(5
D
2
f (x) = ± 2x + 8x + 5
$16:(5
B
4
2
f (x) = x ± 3x + 6x
$16:(5
A
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3
2
f (x) = ± 4x ± 4x + 8
$16:(5
Page 3