Question

find the values of p and q if (x- 1) and (x+2) are factors of the polynomial 2x^3 + px^2 + qx - 14

Answer 1

Use the factors x=1 and x=-2 and synthetic division:

x=1:

1 | 2       p      q      |       -14

     2       2  p+2     | p+q+2

     2  p+2  p+q+2 | p+q-12, so p+q=12 to make the remainder zero.

x=-2:

-2 | 2  p+2  |   p+q+2

       2    -4   |  -2p+ 4

       2  p-2   | -p+q+6, so -p+q=-6 to make the remainder zero.

Add the two p-q equations together: 2q=6, q=3 so p=9.

Therefore the third factor is 2x+7.

The original expression evaluates to 2x³+9x²+3x-14.