Question

The binomial x + 2 is one factor of 4x3 - 9x2 - 30x + 8. Use complete sentences to explain how you use (either) polynomial division or synthetic division to find the remaining factors. List the remaining factors.

Answer 1

I already used the synthetic division to get the answer : 4x^3-17x^2+4. but x+2 wasnt a factor? im confused

Answer 2

x+2 being a factor means that -2 is a root of this expression.
and by algebra you must know that the independent coeficient must be divisible by all real roots.
By that you get that all real root must be +/-1,+/-2,+/-4, +/-8.
You can also see that -2 is a root, and 4 is also a root.
But you need to be careful about the coeficient of the highest exponent in this case the 4.
(x+2)(x-4)a=4x^3 - 9x^2 - 30x + 8
u can see the last root as being 1/4.
That gives you the factorization of the expression that is (x+2)(x-4)(4x-1).
I hope it helped