Answer:
a=4
b=-6
Step-by-step explanation:
If P(x) is divisible by x-c, then P(c)=0.
So P(1)=0 implies 1^3+a1^2+1+b=0
and
P(-3)=0 implies (-3)^2+a(-3)^2+-3+b=0
So notice we have a system to solve.
Let's simply it.
First equation:
1^3+a1^2+1+b=0
1+a+1+b=0
2+a+b=0
a+b=-2
Second equation:
(-3)^3+a(-3)^2+-3+b=0
-27+9a-3+b=0
9a+b-30=0
9a+b=30
Let's put our system together:
a+b=-2
9a+b=30
This is setup so if we subtract the equations b will eliminate allowing us to solve for a:
-8a=-32
a=4
If a=4 and a+b=-2, then 4+b=-2 giving us b=-6.
a=4
b=-6
