Quiz about Synthetic Division and Factor Theorem

Question 1

What is the remainder R when the polynomial p(x) is divided by (x-5)?
p(x) = x³- 5x²+ 2x - 10

Accepted Answer

0

Answer

2x-10

Answer

-2x-10

Answer

2x+10

Question 2

Is (x-4) a factor of (x³ +x² -16x-16)?

Accepted Answer

YES

Answer

NO

Question 3

Is (x-3) a factor of

(x³- 3x²+ 2x + 2)?

Accepted Answer

No

Answer

Yes

Question 4

What is the proper way to write the answer for the following problem?

Accepted Answer

2x³-x²-25x-12

Answer

2x⁴-x³-25x²-12x+0

Question 5

Is (x-7) a factor of (x²-5x+14)?

Accepted Answer

No

Answer

Yes

Question 6

Which binomial is a factor of
f(x)= x³ -6x² +3x +10?

Accepted Answer

x + 1

Answer

x + 2

Answer

x + 5

Answer

x + 10

Question 7

What is the remainder when a³ - 4 is divided by a+2?

Accepted Answer

-12

Answer

-2

Answer

-6

Answer

0

Question 8

Find all the factors of x³ -3x² -4x +12 given that -2 is a zero.

Accepted Answer

(x-2) (x+2) (x-3)

Answer

(x-2) (x+2) (x+3)

Answer

(x-2) (x-2) (x+3)

Answer

(x+2) (x+2) (x+3)

Question 9

Use synthetic division to determine f(-3), if
f(x)= (3x³ -5x² -4x +1).

Accepted Answer

-113

Answer

-25

Answer

25

Answer

113

Question 10

Is (x-2) a factor of f(x)= x³-8x²+14x-4?

Accepted Answer

Yes, (x-2) is a factor. The remainder is zero.

Answer

Yes, (x-2) is a factor. There is a remainder.

Answer

No, (x-2) is  not a factor. The remainder is zero.

Answer

No, (x-2) is  not a factor. There is a remainder.

Question 11

If there is no remainder after synthetic division, what does that mean about the denominator?

Accepted Answer

It's a factor of the function

Answer

It's the y-intercept

Answer

It wants to go steady with the numerator

Answer

There are no x-intercepts

Question 12

What should be the order of the polynomial coefficients if
(3x - 4x³ + 6x⁴ + 1) / (x + 3)

Accepted Answer

6   -4   0   3   1

Answer

3   0   -4   6   1

Answer

6   -4   3   1   0

Answer

-6   4   0   -3   -1

Question 13

What is a way to show that (x-5) is a factor of the polynomial

2x⁴- 3x³- 35x²- 9x + 45?

Accepted Answer

You can use synthetic division and show that the remainder is zero

Answer

You can use synthetic division and show that the remainder is 10

Answer

Multiply (x - 5) five times by itself.

Answer

There is no way to show that (x-5) is a factor of 2x⁴- 3x³- 35x²- 9x + 45.

Synthetic Division and Factor Theorem

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