How do you factor the expression $12 x^{3} - 15 x^{2} - 18 x$ $12x^3-15x^2-18x$ ?

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Answer 1 · 2017-01-16T11:22:03

The answer is $= 3 x (4 x + 3) (x - 2)$ $=3x(4x+3)(x-2)$

We start by factorising the common factors

$12 x^{3} - 15 x^{2} - 18 x$ $12x^3-15x^2-18x$

$= x (12 x^{2} - 15 x - 18)$ $=x(12x^2-15x-18)$

$= 3 x (4 x^{2} - 5 x - 6) = 3 x (4 x + 3) (x - 2)$ $=3x(4x^2-5x-6)=3x(4x+3)(x-2)$

We compare $4 x^{2} - 5 x - 6$ $4x^2-5x-6$ to $a x^{2} + b x + c$ $ax^2+bx+c$

We calculate

$Delta=b^2-4ac=25+4*24=121$

$x=(-b+-sqrt(Delta))/(2a)$

$x_1=(5+sqrt121)/8=(5+11)/8=2$

$x_2=(5-11)/8=-6/8=-3/4$

Therefore,

$12x^3-15x^2-18x=3x(4)(x-2)(x+3/4)$

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

How do you factor the expression 12x^3-15x^2-18x12x3−15x2−18x12x^3-15x^2-18x?