Question 31

Explanation

The first polynomial has divisor $x^2 + x - 2$. Factor the divisor

The remainder is $s(x) = ax + b$.

When $x = 1$

When $x = -2$

The second polynomial has divisor $x^2 - 4x + 3$. Factor the divisor

The remainder is $s(x) = 2bx + a - 1$.

When $x = 1$

When $x = 3$

From equations (1) and (3) we obtain

From equation (2) and given $f(-2) = 7$, then

Substitute $b = 1$ into equation (5)

So the value of