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Zanzabum
3 years ago
11

I will give brainliest to correct answer

Mathematics
1 answer:
FromTheMoon [43]3 years ago
6 0

Answer:

D

Step-by-step explanation:

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 x^{1} 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 could be true, 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.

Of the answer choices, the only one that must be true about p(x) is D, that the remainder when p(x) is divided by x−3 is -2.

The final answer is D.

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Answer:

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Step-by-step explanation:

Represent the original number of chocolates by c.  

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Solving this for c, we multiply both sides by 4:  (2/3)c = 8

and then multiply both sides by (3/2):  c = (3/2)(8) = 12

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6 0
3 years ago
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lbvjy [14]

Answer:

Volume of the box = x^3 - 4x^2

Step-by-step explanation:

V = L × W × H

Where,

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W = Width

H = Height

volume of the rectangular prism = length × width × height

Length = x

Width= length = x

Height = x - 4

V = L × W × H

= x * x * (x - 4)

= x^2 (x - 4)

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V = x^3 - 4x^2

Volume of the box = x^3 - 4x^2

8 0
3 years ago
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The yield per acre will be given by:
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8 0
3 years ago
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Help ASAP I need help with this
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x/y

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3 years ago
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