When $x^4 + 4x^3 +px^2 +qx + 5$ is divided by $x^2 - 1$ the remainder is 2x+3, how do you find the values of p and q?

Question

5422 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-25T21:07:44

Do the division (very carefully).

You'll get a linear remainder $ax+b$ with $a$ and $b$ involving $p$ and $q$ .

Set the remainder from the division equal to $2x+3$ .

The coefficient of $x$ must be $2$ and the constant must be $3$ .

When x^4 + 4x^3 +px^2 +qx + 5x^4 + 4x^3 +px^2 +qx + 5 is divided by x^2 - 1x^2 - 1 the remainder is 2x+3, how do you find the values of p and q?