Question

(x+2) is factor of mx^3+nx^2+x-6.it leaves the remainder 4 when divided by (x-2).find m and n

Answer 1

Answer is in the photo attached check it out!!!!

Answer 2

Answer:

m=0, n=2

Step-by-step explanation:

1. If x+2 is a factor of mx^3+nx^2+x-6, then at x=-2,we have:

m*(-2)^3+n*(-2)^2-2-6=0 =>

-8m+4n-8=0 =>

n=2m+2

2. mx^3+nx^2+x-6, when divided by (x-2), leaves reminder 4, so

(x-2) is the factor of mx^3+nx^2+x-6 - 4 , then we have, x=2 and:

m*2^3+n*2^2+2-10=0 =>

8m+4n-8=0 =>

n=2-2m

We now can compare the 2 values of n, in order to find the value of m:

2m+2=2-2m => 4m=0 => m=0

Now we find n:

n=2*0+2=2

So m =0, n=2