EXPLANATION
If x+2 is a factor, we need to equal the factor to zero, isolate x and substitute the value into the function:
[tex]x+2=0\text{ --> x=-2}[/tex]
Plugging in x=-2 into the function:
[tex]P(-2)=(-2)^4-2(-2)^2+3m(-2)+64[/tex]
Computing the powers:
[tex]P(-2)=16-2*4-6m+64[/tex]
Multiplying numbers:
[tex]P(-2)=16-8-6m+64[/tex]
Adding numbers:
[tex]P(-2)=72-6m=0[/tex]
Adding +6m to both sides:
[tex]72=6m[/tex]
Dividing both sides by 6:
[tex]\frac{72}{6}=m[/tex]
Simplifying:
[tex]12=m[/tex]
In conclusion, the value of m is 12
