Quiz about Polynomial Synthetic Division and Multiplication

Question 1

In order for you to use synthetic division on this problem, what must be done to the dividing factor BEFORE using it?

Accepted Answer

Change the sign of the factor

Answer

Nothing

Answer

Divide out the factor

Answer

Remove it from the expression

Question 2

When using synthetic division, what operation is performed on the numbers that are outside of the box?

Accepted Answer

Multiplication

Answer

Addition

Answer

Subtraction

Answer

Division

Question 3

When asked to divide two polynomials and you are given a factor what methods can be used? (Select all that apply)

Accepted Answer

Long Division

Accepted Answer

Synthetic Division

Answer

Pascal's Triangle

Answer

Box Method

Question 4

When using synthetic division or long division, what is the final value that is left over called?

Accepted Answer

Remainder

Answer

Coefficient

Answer

Variable

Answer

Factor

Question 5

Question 5.

Accepted Answer

x+8

Answer

x+1

Answer

x-9

Answer

2x+1

Question 6

When using synthetic division to find the zeros of a polynomial, what do you do to the number after the semicolon BEFORE putting into the division?

Accepted Answer

Nothing

Answer

Change the sign

Answer

Multiply

Answer

Add

Question 7

What operation is being done between these two polynomials?

Accepted Answer

Multiplication

Answer

Addition

Answer

Subtraction

Answer

Division

Question 8

Divide using synthetic division

Accepted Answer

Option D is correct

Answer

A.

Answer

B.

Answer

C.

Question 9

Question 9.

Accepted Answer

Option B is correct

Answer

A.

Answer

C.

Answer

D.

Question 10

Which term describes the result of dividing one polynomial by another?

Accepted Answer

Quotient

Answer

Dividend

Answer

Remainder

Answer

Divisor

Question 11

When can synthetic division be used?

Accepted Answer

When the divisor is linear, like $$x-c$$ or $$x+c$$

Answer

When the divisor is quadratic, like $$x^2+2x+1$$

Answer

For any type of divisor

Answer

Only for constant divisors

Question 12

How does synthetic division simplify calculations?

Accepted Answer

It uses only coefficients

Answer

It skips the subtraction step

Answer

It avoids multiplication

Answer

It works for all divisors

Question 13

What does the remainder tell us about a polynomial division?

Accepted Answer

The divisor is not a factor

Answer

The division is complete

Answer

The divisor is a factor

Answer

The dividend is incorrect

Question 14

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 15

Was this problem done correctly?

Accepted Answer

Yes, because if you multiply the answer, x²-2x-8 by x-3 you will get x³-5x²-2x+24

Answer

No, because you are supposed to change the signs.

Answer

Yes, because if you add all of the numbers together you get 3.

Answer

No because when you multiply 3 times 1 you should write it below the 1 in the problem, then add and drop that answer down.

Question 16

If we divide these polynomials using synthetic division, what coefficients should we write on the top row?

Accepted Answer

5, -6, -28, -2

Answer

5, 6, 28, 2

Answer

-5, 6, 28, 2

Answer

-5, -6, -28, -2

Polynomial Synthetic Division and Multiplication

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