Question

For a polynomial p(x), the value of p(3) is −2. Which of the following must be true about p(x)?

A) x−5 is a factor of p(x).
B) x−2 is a factor of p(x).
C) x+2 is a factor of p(x).
D) The remainder when p(x) is divided by x−3 is −2.
@xxemilianaxx helpp

Answer 1

i can help you!

Answer 2

i know the awnser

Answer 3

okay

Answer 4

it D.

Answer 5

:)

Answer 6

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Answer 7

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Answer 8

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Answer 9

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Answer 10

bye now!

Answer 11

If the polynomial p(x) is divided by a polynomial of the form x+k (which accounts for all of the possible answer choices in this question), the result can be written as

\[p(x) x+k =q(x)+ r x+k\]

where q(x) is a polynomial and r is the remainder. Since x+k is a degree-1 polynomial (meaning it only includes x1 and no higher exponents), the remainder is a real number.

Therefore, p(x) can be rewritten as p(x)=(x+k)q(x)+r, where r is a real number.

The question states that p(3)=−2, so it must be true that

−2=p(3)=(3+k)q(3)+r

Now we can plug in all the possible answers. If the answer is A, B, or C, r will be 0, while if the answer is D, r will be −2.

A. −2=p(3)=(3+(−5))q(3)+0
−2=(3−5)q(3)
−2=(−2)q(3)

This could be true, but only if q(3)=1



B. −2=p(3)=(3+(−2))q(3)+0
−2=(3−2)q(3)
−2=(−1)q(3)

This would be right but only if q(3)=2



C. −2=p(3)=(3+2)q(3)+0
−2=(5)q(3)

This could be true, but only if q(3)=
−2
5



D. −2=p(3)=(3+(−3))q(3)+(−2)
−2=(3−3)q(3)+(−2)
−2=(0)q(3)+(−2)

This will always be true no matter what q(3) is


The final answer is D.

Answer 12

yeah

Answer 13

Okayy thx

Answer 14

good job!!!!!