Quiz about Polynomial Zeros Synthetic Division

Question 1

What does this tell me?

Accepted Answer

f(-2)= -27 and -27 is the remainder

Answer

-2 is a solution of the function

Answer

(x+2) is a factor of the function

Answer

(x-2) is a factor of the function

Question 2

How can I tell, when doing synthetic division, if the binomial is a FACTOR of the dividend?

Accepted Answer

The remainder is zero

Answer

They are all factors

Answer

We can't tell

Answer

The remainder is a constant

Question 3

When can we use Synthetic Division to divide polynomials?

Accepted Answer

When dividing by a binomial

Answer

Any time we need to divide.

Answer

When dividing by a trinomial

Question 4

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 5

For synthetic division, what would be the number in the left hand box?

Accepted Answer

2

Answer

0

Answer

1

Answer

3

Question 6

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 7

if f(x) = 3x² -9x -20, find the value of f(5) using synthetic division. This means, what is the remainder.

Accepted Answer

10

Answer

0

Answer

15

Answer

-7

Question 8

When p(x) = 9x⁴- 45x³+ 37x² + x +2 is divided by x - 2, a student can determine the remainder by evaluating p(2). What is the value of p(2)?

Accepted Answer

p(2) = -64

Answer

p(2) = 656

Answer

p(2) = 652

Answer

p(2) = -368

Question 9

Is this division problem worked correctly?

Accepted Answer

This is incorrect!

Answer

This is correct!

Question 10

Cam divided (x⁴ + 3x² - 4x - 2) by factor of (x-2) using synthetic division. His work is shown above. Which best describes his mistake?

Accepted Answer

Cam did not use a zero place holder for the x³ term.

Answer

Cam wrote the remainder incorrectly.

Answer

Cam added instead of subtracting the rows.

Answer

Cam should have used -2 as his division since the factor was x-2.

Question 11

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

Accepted Answer

2x³-x²-25x-12

Answer

2x³-x²-25x+12

Answer

2x⁴-x³-25x²-12x+0

Answer

2x⁴-x³-25x²-12x-0

Question 12

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 13

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 14

Is the binomial k - 9 a factor of 4x² -33x -27?

Accepted Answer

yes

Answer

no

Question 15

What would be the coefficients we use to solve:

$$\frac{\left(5x^7+3x^6-9x^4+4x^3+2x-37\right)}{x+1}$$

Accepted Answer

$$5,\ \ 3,\ \ 0,-9,\ \ 4,\ \ 0,\ \ 2,-37$$

Answer

$$5,\ \ 3,-9,\ \ 4,\ \ 2,-37$$

Answer

$$5,\ \ 3,\ \ 0,-9,\ \ 4,\ \ 2,-37$$

Answer

$$5,\ \ 3,\ \ 0,-9,\ \ 4,\ \ 2$$

Question 16

Was this problem done correctly?

Accepted Answer

Yes

Answer

No

Question 17

Was this problem done correctly?

Accepted Answer

Yes

Answer

No

Question 18

Was this problem done correctly and is the answer the correct interpretation?

Accepted Answer

Yes

Answer

No

Question 19

What is the next step?

Accepted Answer

bring down the -20

Answer

Write remainder of 4x

Answer

there is nothing more to do

Answer

multiply by 4

Question 20

After bringing down the -20, we should do what?

Accepted Answer

multiply the binomial out front by +4

Answer

Write remainder of 4x-20

Answer

there is nothing more to do

Answer

Multiply the binomial out front by -4

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