Question

if (x+2) &(x-1) are factors of (x^3+10x^2+mx+n),find the value of m &n

Answer 1

This is the answer for the question

Answer 2

let imagine
p(x) = x^3+10x^2+mx+n
g(x) = (x+2) or (x-1)
if g(x) is the factor of p(x) then p(g) = 0

according to the factor theorem
x+2 = 0
x = -2.
x-1 = 0
x = 1

x^3+10x^2+mx+n = 0
(-2)³+10(-2)²+m(-2)+n = 0
-8+10(4)-2m +n = 0
-8+40-2m+n = 0
32-2m+n = 0
-2m+n = -32 __________(1)

x^3+10x^2+mx+n = 0
(1)³+10(1)²+m(1)+n = 0
1+10+m+n = 0
11+m+n = 0
m+n = -11 ____________(2)

substract equation (1) and (2)
-2m+n = -32
m+n = -11
(-). (-). (+)
____________
-3m + 0 = -21
-3m = -21
m = -21/-3
m = 7

fill value of m in any equation

m+n = -11
7+n = -11
n = -11-7
n = -18

so value of
m and n is 7 and -18 respectively