I'm self-studying from Stroud & Booth's amazing "Engineering Mathematics" and I am stuck on factorizing a particular polynomial to a product of three linear factors. Through the trial-and-error method, I've gotten that the factors are $(x+2)$ and $(x+4)$ (although, it is my understanding that only quadratic polynomials are candidate for looking for multiple factors in this way, in case the factor isn't already given).
I've been banging my head against this, and gotten a different result every time, and the best I could come up with is:
$$(x+1)(x+4)(2x+5).$$
It just seems that every time I try it out, a different result comes out.
Can anybody help me out or give me some pointers? Generally I have this down pretty well, but this particular one is doing my head in.
Best Answer
It's actually $$2x^3+7x^2-14x-40=(2x\color{red}-5)(x+\color{red}2)(x+4)$$
Once you've identified that $(x+2)$ and $(x+4)$ are factors, use the polynomial long division to obtain the last factor.