(x+2) and (x-1) are factors of (x 3 + 10x 2 +mx +n) find m and n
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x+2=0
x=(-2)
also,
x-1=0
x=1
p(-2)=p(1) (since both are factors of p(x))
(-2)^3+10(-2)^2+m(-2)+n=1^3+10(1)^2+m(1)+n
-8+40-2m+n=1+10+m+n
-2m+n-n-m=11+8-40
-3m=(-21)
m=(-21)/(-3)
m=7
Now,
p(1)=0
1^3+10(1)^2+(7)(1)+n=0
1+10+7+n=0
18+n=0
n=(-18)
Therefore m=7 and n=(-18)
x=(-2)
also,
x-1=0
x=1
p(-2)=p(1) (since both are factors of p(x))
(-2)^3+10(-2)^2+m(-2)+n=1^3+10(1)^2+m(1)+n
-8+40-2m+n=1+10+m+n
-2m+n-n-m=11+8-40
-3m=(-21)
m=(-21)/(-3)
m=7
Now,
p(1)=0
1^3+10(1)^2+(7)(1)+n=0
1+10+7+n=0
18+n=0
n=(-18)
Therefore m=7 and n=(-18)
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