Question

How do you factor {eq}f(x) = 4x^4 + 5x^3 + 9x^2 + 10x + 2?

{/eq}

EXPERT ANSWER

Given {eq}f(x) = 4x^4 + 5x^3 + 9x^2 + 10x + 2.

{/eq}

By trial and error method we get {eq}x=-1

{/eq} is a root of {eq}f(x) =0

{/eq} since {eq}4(-1)^4 + 5(-1)^3 + 9(-1)^2 + 10(-1) + 2=0.

{/eq}

Thus {eq}x+1

{/eq} is a factor of {eq}f(x) = 4x^4 + 5x^3 + 9x^2 + 10x + 2.

{/eq}

Now applying long division to