Answer:
a=3
b=24
Step-by-step explanation:
If is a factor of
, then the factors of
must also be factors of
.
So what are the factors of ? Well the cool thing here is the coefficient of
is
.
The zeros of are therefore x=-4 and x=3. We know those are zeros of
by the factor theorem.
So x=-4 and x=3 are also zeros of because we were told that
was a factor of it.
This means that when we plug in -4, the result will be 0. It also means when we plug in 3, the result will be 0.
Let's do that.
Equation 1.
Equation 2.
Let's simplify Equation 1 a little bit:
Let's simplify Equation 2 a little bit:
So we have a system of equations to solve:
16a-b=24
9a-b=3
---------- This is setup for elimination because the b's are the same. Let's subtract the equations.
16a-b=24
9a-b= 3
------------------Subtracting now!
7a =21
Divide both sides by 7:
a =3
Now use one the equations with a=3 to find b.
How about 9a-b=3 with a=3.
So plug in 3 for a.
9a-b=3
9(3)-b=3
27-b=3
Subtract 27 on both sides:
-b=-24
Multiply both sides by -1:
b=24
So a=3 and b=24