Polynomial
Operations
100 A B C D E
Evaluating Polynomia
ls200 A B C D E
Factoring & Solving Polynomia
ls
300 A B C D E
App. Problems
& Theorems
400 A B C D E
Polynomial Graphs
500 A B C D E
Divide (2x 4 – 15x 2 – 10x + 5)
by (x – 3) using long division
Divide (2x 4 – 15x 2 – 10x + 5)
by (x – 3) using long division
100 D
Divide (x 3 + 5x 2 – 8x + 28)
by (5 x – 1) using synthetic division
Divide (x 3 + 5x 2 – 8x + 28)
by (5 x – 1) using synthetic division
100 E
If f(x) = 4x 3 – 5x 2 + 7x - 9,
use synthetic substitution to find f(2)
If f(x) = 4x 3 – 5x 2 + 7x - 9,
use synthetic substitution to find f(2)
200 C
If f(x) = 4x 3 – 5x 2 + 7x - 9,
use synthetic substitution to find f(-
3)
If f(x) = 4x 3 – 5x 2 + 7x - 9,
use synthetic substitution to find f(-
3)
200 D
If f(x) = 3x3 – 7x2 + 2x + 3,
use synthetic substitution to find f( )
If f(x) = 3x3 – 7x2 + 2x + 3,
use synthetic substitution to find f( )
200 E
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13
A rectangle has a perimeter of 80 cm. If its
width is x, express its area in terms of x. What is the maximum area of
the rectangle?
A rectangle has a perimeter of 80 cm. If its
width is x, express its area in terms of x. What is the maximum area of
the rectangle?
400 A
The volume of a box is given by V(x) = x(10 – x)
(10 – 2x). Find the approx. max. volume.
The volume of a box is given by V(x) = x(10 – x)
(10 – 2x). Find the approx. max. volume.
400 B
An open box is to be formed by cutting squares from a square sheet of 10 cm on each side. Find the value of x that maximizes
the volume.
An open box is to be formed by cutting squares from a square sheet of 10 cm on each side. Find the value of x that maximizes
the volume.
400 C
A polynomial equation with rational coefficients
has the given roots. Find 2 additional roots.
– and 5 +
A polynomial equation with rational coefficients
has the given roots. Find 2 additional roots.
– and 5 +
400 D
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7
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2
A polynomial equation with rational coefficients has the given roots. Find
2 additional roots.– 7i and 3 + 7i
A polynomial equation with rational coefficients has the given roots. Find
2 additional roots.– 7i and 3 + 7i
400 E
Determine the max. number of zeros and
vertices of the polynomial
P(x) = 12x 6 + 6x 4 – 8x
Determine the max. number of zeros and
vertices of the polynomial
P(x) = 12x 6 + 6x 4 – 8x
500 B
Given the polynomial P(x) = (x – 5) (x + 6) 4,
where is the graph tangent and where
does it cross the x-axis?
Given the polynomial P(x) = (x – 5) (x + 6) 4,
where is the graph tangent and where
does it cross the x-axis?
500 C
Given the polynomial P(x) = – 5x 2 + 7x – 9,
describe the behavior of the graph on the
right and left
Given the polynomial P(x) = – 5x 2 + 7x – 9,
describe the behavior of the graph on the
right and left
500 D
Sketch the graph of f(x) = (x + 1)(x – 1)(x –
2)
Sketch the graph of f(x) = (x + 1)(x – 1)(x –
2)
500 E
(11x 5 + 7x 4 – 5x 3) +
(12x 6 + 6x 4 – 8x)
(11x 5 + 7x 4 – 5x 3) +
(12x 6 + 6x 4 – 8x)
12x 6 + 11x 5 + 13x 4 – 5x 3 – 8x12x 6 + 11x 5 + 13x 4 – 5x 3 – 8x
100 A
(3x 2 + 7x – 4) – (10x 2 + 15x + 7)(3x 2 + 7x – 4) – (10x 2 + 15x + 7)
- 7x 2 – 8x – 11- 7x 2 – 8x – 11
100 B
Multiply (3 x 2 + 2 x + 5)
by (5 x + 6)
Multiply (3 x 2 + 2 x + 5)
by (5 x + 6)
12x 6 + 11x 5 + 13x 4 – 5x 3 – 8x12x 6 + 11x 5 + 13x 4 – 5x 3 – 8x
100 C
Divide (2x 4 – 15x 2 – 10x + 5)
by (x – 3) using long division
Divide (2x 4 – 15x 2 – 10x + 5)
by (x – 3) using long division
Q: 2x 3 + 6x 2 + 3x – 1R: 2
Q: 2x 3 + 6x 2 + 3x – 1R: 2
100 D
Divide (x 3 + 5x 2 – 8x + 28)
by (5 x – 1) using synthetic division
Divide (x 3 + 5x 2 – 8x + 28)
by (5 x – 1) using synthetic division
Q: x 2 + 3x – 1R: 0
Q: x 2 + 3x – 1R: 0
100 E
Evaluate f(x) = 3 x 2 – 5 x + 6
for f(2i)
Evaluate f(x) = 3 x 2 – 5 x + 6
for f(2i)
- 2 – 10i- 2 – 10i
200 A
If f(x) = 4x 3 – 5x 2 + 7x - 9,
use synthetic substitution to find f(2)
If f(x) = 4x 3 – 5x 2 + 7x - 9,
use synthetic substitution to find f(2)
1717
200 C
If f(x) = 4x 3 – 5x 2 + 7x - 9,
use synthetic substitution to find f(-
3)
If f(x) = 4x 3 – 5x 2 + 7x - 9,
use synthetic substitution to find f(-
3)- 183- 183
200 D
If f(x) = 3x3 – 7x2 + 2x + 3,
use synthetic substitution to find f( )
If f(x) = 3x3 – 7x2 + 2x + 3,
use synthetic substitution to find f( )
33
200 E
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13
Solve3x4 + 12x2 – 15 = 0
Solve3x4 + 12x2 – 15 = 0
x = 1; x = - 1; x =x = 1; x = - 1; x =
300 D
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– 5
Solvex3 – 5x2 + 4x – 20 = 0
Solvex3 – 5x2 + 4x – 20 = 0
x = 2; x = - 2; x = 5x = 2; x = - 2; x = 5
300 E
A rectangle has a perimeter of 80 cm. If its
width is x, express its area in terms of x. What is the maximum area of
the rectangle?
A rectangle has a perimeter of 80 cm. If its
width is x, express its area in terms of x. What is the maximum area of
the rectangle?x(40 – x); 400 cm 2x(40 – x); 400 cm 2
400 A
The volume of a box is given by V(x) = x(10 – x)
(10 – 2x). Find the approx. max. volume.
The volume of a box is given by V(x) = x(10 – x)
(10 – 2x). Find the approx. max. volume.
x = 1.67; 9.26 ft 3x = 1.67; 9.26 ft 3
400 B
An open box is to be formed by cutting squares from a square sheet of 10 cm on each side. Find the value of x that maximizes
the volume.
An open box is to be formed by cutting squares from a square sheet of 10 cm on each side. Find the value of x that maximizes
the volume.x = 1.7; 74.1 cm 3x = 1.7; 74.1 cm 3
400 C
A polynomial equation with rational coefficients
has the given roots. Find 2 additional roots.
– and 5 +
A polynomial equation with rational coefficients
has the given roots. Find 2 additional roots.
– and 5 +
and 5 – and 5 –
400 D
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7
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2
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7
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2
A polynomial equation with rational coefficients has the given roots. Find
2 additional roots.– 7i and 3 + 7i
A polynomial equation with rational coefficients has the given roots. Find
2 additional roots.– 7i and 3 + 7i
7i and 3 – 7i7i and 3 – 7i
400 E
Determine the max. number of zeros and
vertices of the polynomial
P(x) = 12x 6 + 6x 4 – 8x
Determine the max. number of zeros and
vertices of the polynomial
P(x) = 12x 6 + 6x 4 – 8x6 zeros; 5 vertices6 zeros; 5 vertices
500 B
Given the polynomial P(x) = (x – 5) (x + 6) 4,
where is the graph tangent and where
does it cross the x-axis?
Given the polynomial P(x) = (x – 5) (x + 6) 4,
where is the graph tangent and where
does it cross the x-axis?Tangent @ - 6;
crosses @ 5Tangent @ - 6;
crosses @ 5
500 C
Given the polynomial P(x) = – 5x 2 + 7x – 9,
describe the behavior of the graph on the
right and left
Given the polynomial P(x) = – 5x 2 + 7x – 9,
describe the behavior of the graph on the
right and leftRises to the left & falls to the rightRises to the left & falls to the right
500 D