Find the polynomial if given q(x) = x(^2) – x – 5, d(x) = 3x – 1 and r(x) = 7.
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A.
3x(^3) – 4x(^2) – 14x + 12 -
B.
3x(^2) + 3x – 7 -
C.
3x(^3) + 4x(^2) + 14x – 12 -
D.
3x(^2) – 3x + 4
Correct Answer: Option A
Explanation
Given q(x) [quotient], d(x) [divisor] and r(x) [remainder], the polynomial is gotten by multiplying the quotient and the divisor and adding the remainder.
i.e In this case, the polynomial = (x(^2) – x – 5)(3x – 1) + 7.
= (3x(^3) – x(^2) – 3x(^2) + x – 15x + 5) + 7
= (3x(^3) – 4x(^2) – 14x + 5) + 7
= 3x(^3) – 4x(^2) – 14x + 12
There is an explanation video available below.