Question

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

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

Answer 1

The correct option is C

7 and -18

x + 2 and x - 1 are the factors of

f(x) = $x^3+10x^2$ + mx + n

Let x + 2 = 0, then x =-2

$\therefore f(-2)=(-2{)}^3+10(-2{)}^2$ + m (-2) + n

=-8 + 40 - 2m + n = 32 - 2m + n

$\therefore$ x + 2 is a factor of f(x)

$\therefore$ Remainder = 0

$\therefore$ 32-2m+n=0 $\Rightarrow$ 2m - n = 32 ....(i)

Again x - 1 is a factor of f(x)

Let x - 1=0, then x = 1

$\therefore$ f(1) $=(1{)}^3+10(1{)}^2+m\times$ 1 + n

= 1 + 10 + m + n = m + n = - 11 ....(ii)

Adding (i) and (ii),

3m = 32 - 11 =21

$\Rightarrow m=\frac{21}{3}$ = 7 and n = - 11 - m = - 11 - 7 = - 18

$\therefore$ m =7, n = -18