Question

If the polynomial $y^3-5y^2+7y+m$ is divided by y + 2 and the remainder is 50 then find the value of m.

Answer 1

Let $p\left(y\right)=y^3-5y^2+7y+m$.

When the polynomial is divided by (y + 2), the remainder is 50. This means that the value of the polynomial when y = −2 is 50.

By remainder theorem,

Remainder = p(−2) = 50

$$\begin{gathered} \therefore {\left(-2\right)}^3-5\times {\left(-2\right)}^2+7\times \left(-2\right)+m=50 \\ \Rightarrow -8-5\times 4-14+m=50 \\ \Rightarrow -8-20-14+m=50 \\ \Rightarrow -42+m=50 \\ \Rightarrow m=50+42=92 \end{gathered}$$
Thus, the value of m is 92.