Factors

Algebra Level 1

Factorize 18 x 3 + 3 x 2 − 6 x 18x^3+3x^2-6x .

( 3 x − 4 ) ( 6 x − 5 ) (3x - 4)(6x - 5) ( 5 x − 2 ) ( 2 x + 1 ) (5x - 2)(2x + 1) 3 x ( 2 x − 1 ) ( 3 x + 2 ) 3x(2x - 1)(3x + 2) 2 ( x − 1 ) ( 3 x − 5 ) 2(x - 1)(3x - 5) ( 2 x + 5 ) ( 2 x + 1 ) (2x + 5)(2x + 1)

Britney Florian by britney florian , 19, USA

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4 solutions

Sabhrant Sachan
Jul 15, 2016

3 x ( 2 x − 1 ) ( 3 x + 2 ) 3x(2x-1)(3x+2) is the only cubic polynomial

5 Helpful 0 Interesting 0 Brilliant 0 Confused

Bwahahahaha nice solution

Hung Woei Neoh - 4 years, 11 months ago

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Hehe yeah well if the multiple choice answer is stated this was I always check wat can't be the case... so this leaves only 1 answer here. Just stupid choices :)

Peter van der Linden - 4 years, 10 months ago
Munem Shahriar
May 26, 2017

18 x 3 + 3 x 2 − 6 x 18x^3+3x^2-6x

= 3 x ( 6 x 2 + x − 2 ) = 3x ( 6x^2 + x - 2 )

= 3 x ( 6 x 2 + 4 x − 3 x − 2 ) = 3x (6x^2 + 4x - 3x - 2)

= 3 x { 2 x ( 3 x + 2 ) − 1 ( 3 x + 2 ) } = 3x \{2x (3x + 2) - 1 (3x + 2)\}

= 3 x ( 3 x + 2 ) ( 2 x − 1 ) = 3x (3x + 2) (2x - 1)

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Hung Woei Neoh
Jul 16, 2016

18 x 3 + 3 x 2 − 6 x = 3 x ( 6 x 2 + x − 2 ) = 3 x ( 6 x 2 + 4 x − 3 x − 2 ) = 3 x ( 2 x ( 3 x + 2 ) − 1 ( 3 x + 2 ) ) = 3 x ( 2 x − 1 ) ( 3 x + 2 ) 18x^3+3x^2-6x\\ =3x(6x^2+x-2)\\ =3x(6x^2+4x-3x-2)\\ =3x\big(2x(3x+2)-1(3x+2)\big)\\ =\boxed{3x(2x-1)(3x+2)}

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Lew Sterling Jr
May 21, 2019

18 x 3 + 3 x 2 − 6 x = 3 x ( 6 x 2 + x − 2 ) = 3 x ( 6 x 2 − 3 x + 4 x − 2 ) = 3 x ( ( 6 x 2 − 3 x ) + ( 4 x − 2 ) ) = 3 x ( 3 x ( 2 x − 1 ) + 2 ( 2 x − 1 ) ) = 3 x ( 2 x − 1 ) + 2 ( 2 x − 1 ) \begin{matrix} 18x^3+3x^2-6x\\ =3x\left(6x^2+x-2\right)\\ =3x\left(6x^2-3x+4x-2\right)\\ =3x(\left(6x^2-3x\right)+\left(4x-2\right))\\ =3x(3x\left(2x-1\right)+2\left(2x-1\right))\\ =\mathbf{3x\left(2x-1\right)+2\left(2x-1\right)} \end{matrix}

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