Question

On dividing r" - 3x2 + x + 2 by a polynomial g(x), the quotient and remainder were x-2 and 2x+4, respectively.
Find g(x).​

Answer 1

Step-by-step explanation:

Divident = Divisor×Quotient + Remainder

$3 {x}^{2} + x + 2 = g(x) \times x - 2 + (2x + 4) \\ 3 {x}^{2} + x + 2 - 2x - 4 = g(x) \times x - 2 \\ 3 {x}^{2} - x - 2 = g(x) \times x - 2 \\ g(x) = \frac{3 {x}^{2} - x - 2}{x - 2}$