Quiz about Polynomial Roots

Question 1

When would it be appropriate to use the $$\pm$$ symbol?

Accepted Answer

$$x^2=16$$

Answer

$$\sqrt[]{16}$$

Answer

$$4^2=x$$

Answer

$$\left(-4\right)^2=x$$

Question 2

If you were dividing x⁶ + 4x³ + 2, how many 0's would you need when setting up the top row of your synthetic division?

Accepted Answer

4

Answer

0

Answer

2

Answer

6

Question 3

x²+ 12x + 32 = 0

Accepted Answer

x = -4, -8

Answer

x = -4, 8

Answer

x = 4, 8

Answer

x = 0, 12

Question 4

All imaginary roots comes in pairs.

Accepted Answer

True

Answer

False

Question 5

Simplify the following expression:

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 6

Solve for all zeros:

$$x\left(x-1\right)\left(x+2\right)\left(3x-5\right)\left(x^2+1\right)\ =\ 0$$

Accepted Answer

$$x=0,\ 1,\ -2,\ \frac{5}{3},\ \pm i$$

Answer

$$x=-1,\ 2,\ -\frac{5}{3},\ \pm i$$

Answer

$$x=0,\ -1,\ 2,\ -\frac{5}{3},\ \pm i$$

Answer

No solution

Question 7

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

Accepted Answer

5

Answer

8

Answer

9

Answer

3

Question 8

The degree of the polynomial determines the number of roots.

Accepted Answer

True

Answer

False

Question 9

Which of these is a possible rational root of the polynomials?

x³ - 6x² - x + 30

Accepted Answer

-15

Answer

0

Answer

4

Answer

-9

Question 10

Is (x-3) a factor of
(x³- 3x²+ 2x + 2)?

Accepted Answer

No

Answer

Yes

Question 11

If 2i is a zero, then

Accepted Answer

-2i is a zero too

Answer

2i repeats twice

Answer

1-2i is a zero too

Answer

0+2i is a zero too

Question 12

If a polynomial has a degree of 4, what can you say about its roots?

Accepted Answer

It can have 4 real roots, or a combination of real and imaginary roots.

Answer

It must have exactly 4 real roots.

Answer

It can have at most 2 real roots.

Answer

It cannot have any real roots.

Question 13

What is synthetic division used for in polynomials?

Accepted Answer

A simplified method for dividing polynomials and finding roots

Answer

A method for adding polynomials

Answer

A technique for factoring polynomials

Answer

A way to graph polynomial functions

Question 14

What is the factored form of a polynomial with roots at 1, -3, and 4?

Accepted Answer

(x - 1)(x + 3)(x - 4)

Answer

(x + 1)(x - 3)(x + 4)

Answer

(x - 1)(x - 3)(x + 4)

Answer

(x + 1)(x + 3)(x - 4)

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