How do you factor $2x^3 + x^2 - 4x - 3$ ?

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Answer 1 · 2015-05-30T17:37:14

First notice that $x=-1$ is a root of $2x^3+x^2-4x-3 = 0$ .

That is: if you substitute $-1$ for $x$ in the polynomial then the result is $0$

So $(x+1)$ is a factor of $2x^3+x^2-4x-3$ .

Use synthetic division by this factor...

$2x^3+x^2-4x-3 = (x+1)(2x^2-x-3)$

Notice that $-1$ is also a root of $2x^2-x-3=0$ , so we have another $(x+1)$ factor...

$(2x^2-x-3) = (x+1)(2x-3)$

So $2x^3+x^2-4x-3 = (x+1)(x+1)(2x-3)$

How do you factor 2x^3 + x^2 - 4x - 32x^3 + x^2 - 4x - 3?