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

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Answer 1 · 2015-10-25T21:07:44

Do the division (very carefully).

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

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

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

When x4+4x3+px2+qx+5x^4 + 4x^3 +px^2 +qx + 5 is divided by x2−1x^2 - 1 the remainder is 2x+3, how do you find the values of p and q?