Synthetic Division and the Remainder Theorem Answers
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1
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Use synthetic division to solve . What is the quotient?
A
3 x cubed + 12 x squared + 26 x + 61 + StartFraction 132 Over x + 2 EndFraction
B
3 x cubed + 2 x + 5
C
3 x cubed + 12 x squared + 26 x + 61 + StartFraction 132 Over x minus 2 EndFraction
D
3 x Superscript 4 Baseline + 2 x squared + 5 x
2
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If f(1) = 0, what are all the roots of the function ? Use the Remainder Theorem.
A
x = –1, x = 1, or x = 3B
x = –3, x = –1, or x = 1C
x = –3 or x = 1D
x = –1 or x = 33
The volume of a rectangular prism is with height x + 2. Using synthetic division, what is the area of the base?
A
2 x cubed + 13 x squared + 18 x
B
2 x cubed + 5 x squared minus 18 x
C
2 x squared + 13 x + 18
D
2 x squared + 5 x minus 18
4
One factor of is (x + 7). What are all the roots of the function? Use the Remainder Theorem.
A
x = –4, x = –2, or x = 7B
x = –7, x = 2, or x = 4C
x = –7, x = 5, or x = 280D
x = –280, x = –5, or x = 75
What divisor is represented by the synthetic division below?
A
–5B
5C
x + 5D
x – 56
Use synthetic division to solve . What is the quotient?
A
4 x squared minus 27 x + 167 minus StartFraction 996 Over x minus 6 EndFraction
B
4 x squared + 21 x + 131 + StartFraction 792 Over x + 6 EndFraction
C
4 x squared + 21 x + 131 + StartFraction 792 Over x minus 6 EndFraction
D
4 x squared minus 27 x + 167 minus StartFraction 996 Over x + 6 EndFraction
7
If –1 is a root of f(x), which of the following must be true?
A
A factor of f(x) is (x – 1).B
A factor of f(x) is (x + 1).C
Both (x – 1) and (x + 1) are factors of f(x).D
Neither (x – 1) nor (x + 1) is a factor of f(x).8
If (x + 8) is a factor of f(x), which of the following must be true?
A
Both x = –8 and x = 8 are roots of f(x).B
Neither x = –8 nor x = 8 is a root of f(x).C
f(–8) = 0D
f(8) = 09
What dividend is represented by the synthetic division below?
A
Negative 10 x squared minus 5
B
2 x cubed + 10 x squared + x + 5
C
2 x squared + 1
D
2 x cubed + x
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