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How do you factor the expression #12x^3-15x^2-18x#?

Answer 1

Eva Adamson

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

We start by factorising the common factors

#12x^3-15x^2-18x#

#=x(12x^2-15x-18)#

#=3x(4x^2-5x-6)=3x(4x+3)(x-2)#

We compare #4x^2-5x-6# to #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)#

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Answer 2

Isaiah Anthony

To factor the expression 12x^3 - 15x^2 - 18x, you can first factor out the greatest common factor, which is 3x. After factoring out 3x, you'll have 3x(4x^2 - 5x - 6). Then, you can further factor the quadratic expression inside the parentheses using methods like factoring by grouping, the quadratic formula, or completing the square. In this case, the quadratic expression can be factored into (4x - 6)(x + 1). So, the fully factored expression is 3x(4x - 6)(x + 1).

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.