Find the polynomial if given q(x) = x2 2 - x - 5, d(x) = 3x - 1 and r(x) = 7.

Answer Details

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