Synthetic Division and the Remainder Theorem Answers

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Use synthetic division to solve . What is the quotient?

4 x squared minus 27 x + 167 minus StartFraction 996 Over x minus 6 EndFraction

4 x squared + 21 x + 131 + StartFraction 792 Over x + 6 EndFraction

4 x squared + 21 x + 131 + StartFraction 792 Over x minus 6 EndFraction

4 x squared minus 27 x + 167 minus StartFraction 996 Over x + 6 EndFraction

One root of is x = 2. What are all the roots of the function? Use the Remainder Theorem.

x = 2, x = 3, or x = 4

x = –2, x = –3, or x = –4

x = 1, x = 2, x = 3, or x = 13

x = –1, x = –2, x = –3, or x = –13

If f(1) = 0, what are all the roots of the function ? Use the Remainder Theorem.

x = –1, x = 1, or x = 3

x = –3, x = –1, or x = 1

x = –3 or x = 1

x = –1 or x = 3

What divisor is represented by the synthetic division below?

–5

x + 5

x – 5

Use synthetic division to solve . What is the quotient?

2 x squared minus 2 x minus 29 + StartFraction 102 Over x + 3 EndFraction

2 x squared minus 2 x minus 29 + StartFraction 102 Over x minus 3 EndFraction

2 x cubed + 10 x squared minus 5 x

2 x squared + 10 x minus 5

If –1 is a root of f(x), which of the following must be true?

A factor of f(x) is (x – 1).

A factor of f(x) is (x + 1).

Both (x – 1) and (x + 1) are factors of f(x).

Neither (x – 1) nor (x + 1) is a factor of f(x).

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