Question

given a polynomial and one of its factors, find the remaining factors of the polynomial. some factors may not be binomials. use long division.

Answer 1

Find attached solution. Cheers.

The second quadratic function is not factorisable, so we leave it that way.

Cheers.

Answer 2

This is easy to do because you can factor
example
6/2=3 because 6=2*3 so 6/2=3/1 times 2/2 or 3

2x^3+17x^2+23x-42 can be factored out to equal
(x-1)(x+6)(2x+7)

so [(x-1)(x+6)(2x+7)]/(2x+7)=[(x-1)(x+6)] times (2x+7)/(2x+7)=(x-1)(x+6)=x^2+5x-6

the answer is (x-1)(x+6) or x^2+5x-6