Factorise completely $2x^3 - 13x^2 + 6x$ . Answer ...

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Worked solution

1. Extract the common factor from all terms.

$2x^3-13x^2+6x=x(2x^2-13x+6)$

2. Factorise the quadratic expression completely.

Find two factors of $2\times 6=12$ that add to $-13$ : $-12$ and $-1$ .

$2x^2-13x+6=2x^2-12x-x+6$
$=2x(x-6)-1(x-6)$
$=(2x-1)(x-6)$

Hence,
$2x^3-13x^2+6x=x(2x-1)(x-6).$

Answer

$x(2x-1)(x-6)$

AI analysis — may contain mistakes.

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