How do you factor $6x^3+21x^2+15x$ ?

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Answer 1 · 2015-06-26T18:49:57

$6x^3+21x^2+15x = 3x(2x^2+7x+5)$

$=3x(2x+5)(x+1)$

Given $6x^3+21x^2+15x$

First notice that all of the terms are divisible by $3x$ , so separate out that as a factor first:

$6x^3+21x^2+15x = 3x(2x^2+7x+5)$

Let $f(x) = 2x^2+7x+5$

First notice that $2-7+5 = 0$ , so $f(-1) = 0$ , so $(x+1)$ is a factor of $f(x)$

The remaining factor must be $(2x+5)$ in order that the coefficient $2$ of $x^2$ and the constant term $5$ result:

$2x^2+7x+5 = (2x+5)(x+1)$

Putting it all together:

$6x^3+21x^2+15x = 3x(2x+5)(x+1)$

How do you factor 6x^3+21x^2+15x 6x^3+21x^2+15x ?