Question

If the quotient on dividing, $8x^4-2x^2+6x-7$ by $2x+1$ is $4x^3+p{x}^2-qx+3$, then find $q-p$.

Answer 1

We first divide the polynomial $8x^4-2x^2+6x-7$ by $2x+1$ as shown in the above image:

From the above division, we observe that the quotient is $4x^3-2x^2+3$. Also, the given quotient is $4x^3+p{x}^2-qx+3$. So, comparing the coefficients of $x$ and $x^2$, we get:

$p=-2$ and $q=0$

Therefore, $q-p=0-(-2)=2$

Hence, $q-p=2$.