Question

on dividing the polynomial 2x^3 + ax^2 + 3x - 5 by x - 1 the remainder is 7. find the value of a

Answer 1

When a polynomial $p(x)$ is divided by $x-a$, the remainder is $p(a)$. Here $p(x)=2x^3+ax^2+3x-5$. When $p(x)$ is divided by $x-1$, the remainder according to the above formula is $p(1)=2.1^3+a.1^2+3.1-5=a=7$.

Thus the value of $a=7$