Free Printable Polynomial Equations and Rational Root Theorem 22

1.

Which of the following is a COMPLETE list of all possible Rational Zeros?
f(x) = 3x³ + 2x² - 6x + 7

a)

±1, ±7, ±1/3, ±7/3

b)

±1, 7

c)

±1, ±3, ±7, ±7/3

d)

±1, ±3, ±7, ±1/3, ±7/3

2.

According to the Rational Root Theorem, what are the all possible rational roots?
2x³ - 11x² + 12x + 9 = 0

a)

±1,±2

b)

±1,±3,±9

c)

±1,±3±9,±1/2,±3/2,±9/2

d)

±1,±2,±1/3,±2/3,±1/9,±2/9

3.

Solve by using Rational Root Theorem:
x⁴ - x³ + 2x² - 4x - 8 = 0

a)

-1, 2, ±2

b)

-1, 2, ±2i

c)

1, -2, 4

d)

1, 2, 2i

4.

How many zeros does the following function have?
f(x)= x⁵- 3x³ + x

a)

8

b)

9

c)

5

d)

3

5.

What is the name of the theorem that we've discussed all week?

a)

Pythagorean Theorem

b)

Remainder Theorem

c)

Rational Root Theorem

d)

Einstein's Theory of Relativity

6.

$3x^7-5x^4+7x^2-8=0$

Identify the P and Q values in the equation:

a)

P = -5 ; Q = 3

b)

P = 8; Q = 3

c)

P = -8; Q = 7

d)

P = 3; Q = 8

7.

$2x^4-17x^3+39x^2-35x+11=0$ Find the roots.

a)

{11/2 , 1 mult. 3}

b)

{-1mult. 3, 3/2}

c)

{1, -2, 3/2, 4}

d)

{-1, -2, 5/2, -4}

8.

$4x^4-4x^3-15x^2-2x+5=0$ Find the roots.

a)

{1 mult.2, 5/2, 1/2}

b)

{-1 mult. 2, -1/2, 3/2}

c)

{1 mult. 2, -3/2, -1/2}

d)

{-1 mult. 2, 5/2, 1/2}

9.

$6x^4-11x^3-21x^2-x+3=0$ Find the roots.

a)

{-1, -3, 1/2, 1/3}

b)

{1/3, -1/2, -1, 3}

c)

{1, -1, -3, 1/2}

d)

{-1, -3, 2/3, -1/2}

10.

$4x^4-25x^2+36=0$
Find the roots.

a)

$\pm\frac{3}{2},\ \pm2$

b)

$\pm2,\ \pm\frac{2}{3}$

c)

$1,\ -2,\ -1,\ 3$

d)

$2,\ -3,\ \frac{2}{3},\ -2$

11.

Which of the following includes a name that is NOT one of Santa's reindeer?

a)

Dasher, Dancer, Prancer, Vixen

b)

Comet, Cupid, Rocket, Blitzen

c)

Rudolph, Dasher, Dancer, Vixen

Polynomial Equations and Rational Root Theorem 22

Total questions: 11

Worksheet time: 2hrs 50mins

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