Factorising Polynomial/Cubic

Question

I'm having trouble with this question. Could someone please show me in steps how to factorise this cubic function. Also, is there a simple method to go about solving cubics in general?

$$x^3 + 2x^2 -15x = 0$$

Thanks :)

Answer 1

Hint: First, factor out $x$ then use the quadratic formula

$$x(x^2+2x-15)=0.$$

Answer 2

Factorise out the $x$ first to get $x(x^2+2x-15)=0$ and then factorise the quadratic inside.

Answer 3

In this cubic, $x$ can be factored out as the constant term is zero, i.e.,

$ax^3+bx^2+cx=0$

$x(ax^2+bx+c)=0$

And the quadratic part can be dealt with.

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In the general case,

$ax^3+bx^2+cx+d=0$

• if $a$ and $d$ are non-zero

• and $a$, $b$, $c$ and $d$ are all integers,

you could use the Rational Root Theorem. It's pretty helpful at times.

(https://en.wikipedia.org/wiki/Rational_root_theorem) (Check out the examples given here)

This works for finding roots of cubics or even of higher degree, given that the above-mentioned conditions are satisfied (and the roots actually exist and are rational). This might help you track at least one of the roots of cubics satisfying the conditions.