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SSSSS [86.1K]
3 years ago
10

What is the remainder R when the polynomial p(x) is divided by (x - 2)? Is (x - 2) a factor of p(x)? P(x) = -4x4 + 6x3 + 8x2 - 6

x - 4 A) R = 0, no B) R = 0, yes C) R = -72, no D) R = -72, yes
Mathematics
1 answer:
Trava [24]3 years ago
7 0

Answer:

B

(x-2) is a factor since remainder is 0.

Step-by-step explanation:

We divide (x-2) into the polynomial -4x^4+6x^3+8x^2-6x-4 through long division or synthetic. We choose long division and look for what will multiply with (x-2) to make the polynomial -4x^4+6x^3+8x^2-6x-4 .

(x-2)(-4x^3)=-4x^4+8x^3

We subtract this from the original -4x^4-(-4x^4)+6x^3-(8x^3)+8x^2-6x-4.

This leaves -2x^3+8x^2-6x-4. We repeat the step above.

(x-2)(-2x^2)=-2x^3+4x^2.

We subtract this from -2x^3-(-2x^3)+8x^2-(4x^2)-6x-4=4x^2-6x-4. We repeat the step above.

(x-2)(4x)=4x^2-8x.

We subtract this from 4x^2-(4x^2)-6x-(-8x)-4=2x-4. We repeat the step above.

(x-2)(2)=2x-4.

We subtract this from 2x-(2x)-4-(4)=0. There is no remainder. This means (x-2) is a factor.


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