Find the polynomial if given q(x) = x\(^2\) - x - 5, d(x) = 3x - 1 and r(x) = 7.
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: 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