Question

If x³ + ax² − bx+ 10 is divisible by x² − 3x + 2, find the values of a and b.

Answer 1

Let and be the given polynomials.

We have,

Here, and are the factors of g(x),

Now,

By factor theorem,

and

Subtracting (ii) by (i), we get,

$$\begin{gathered} \left(2a-b\right)-\left(a-b\right)=-9-\left(-11\right) \\ a=2 \end{gathered}$$
Putting this value in equation (ii), we get,

Hence, the value of a and b are 2 and 13 respectively.