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Question

How do you factorize f(x)=2x^3+4x^2+5x+3

to obtain this form of equation f(x)=(x+1)(ax^2+bx+c)?
thanks a lot!!

Answer 1

f(x) = 2x^3 + 4x^2 + 5x + 3

You find a value k = x for which f(x) = 0.

Then, (x - k) is a factor of f(x). Then, by polynomial division, we get the other factor, which will be quadratic.

Here, f(x) = 2x^3 + 4x^2 + 5x + 3

We find that f(x) = 0 when x = -1
So, (x + 1) is a factor of f(x)

By division, we find that,

f(x) = (x + 1)(2x^2 + 2x + 3)

Answer 2

easy