Question

Not sure how to approach this question whether to use the factor theorem or to use the synthetic division

Answer 1

Step-by-step explanation

If x+2 is a factor, we need to equal the factor to zero, isolate x and substitute the value into the function:

`x+2=0\text{ --> x=-2}`

Plugging in x=-2 into the function:

`P(-2)=(-2)^4-2(-2)^2+3m(-2)+64`

Computing the powers:

`P(-2)=16-2*4-6m+64`

Multiplying numbers:

`P(-2)=16-8-6m+64`

Adding numbers:

`P(-2)=72-6m=0`

Adding +6m to both sides:

`72=6m`

Dividing both sides by 6:

`(72)/(6)=m`

Simplifying:

`12=m`

In conclusion, the value of m is 12