Question

If x+2 and x-1 are factors of $x^3+10x^2+mx+n$ then which of the following are the values of m and n respectively?

• A. 5 and - 3
• B. 17 and -8
• C. 7 and -18
• D. 23 and -19

Answer 1

The correct option is C 7 and -18

Here, x + 2 is a factor of $x^3+10x^2+mx+n$
$x=-2$
$(-2{)}^3+10(-2{)}^2+m(-2)+n=0$
$-8+40=2m-n$
$2m-n=\mathrm{32.......}\left(i\right)$
Again, x - 1 is a factor of $x^3+10x^2+mx+n$
$x=1$
$1+10+m+n=0$
$m+n=-\mathrm{11.......}\left(ii\right)$
Adding (i) and (ii). we get,
3m = 21
m = 7
By putting m in (i). we get,
$2\left(7\right)-n=32$
$-n=18$
$n=-18$