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
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
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
Source: Myschool Past Questions Archive (Record #55396)