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Multiply and Simplify

x^2-2x-48  *  9x^3-4x
3x^3-2x^2     8x-64

### 3 Answers by Expert Tutors

Steve S. | Tutoring in Precalculus, Trig, and Differential CalculusTutoring in Precalculus, Trig, and Diffe...
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Multiplying the fractions results in:

f(x)=(x^2-2x-48)(9x^3-4x)/((3x^3-2x^2)(8x-64))

f(x)=x(x-8)(x+6)(9x^2-4)/(8x^2(3x-2)(x-8))

9x^2-4 = (3x)^2-2^2 = (3x+2)(3x–2)

f(x)=x(x-8)(x+6)(3x+2)(3x–2)/(8x^2(3x-2)(x-8))

f(x)=x(x-8)(3x–2)/(x(x-8)(3x–2))
* (x+6)(3x+2)/(8x)

x(x-8)(3x–2)/(x(x-8)(3x–2))
= {1 if x ≠ 0, 2/3, or 8; UNDEFINED otherwise }
I.e., there are “Holes” at x = 0, 2/3, or 8.

f(x)=(x+6)(3x+2)/(8x), x ≠ 0, 2/3, or 8

Since x is in the denominator of this reduced form there will be a vertical asymptote at x = 0.

f(x)=(3x^2+20x+12)/(8x), x ≠ 0, 2/3, or 8

Do long division of numerator by denominator:

3x^2+20x+12 | 3x/8
3x^2
––––––––––––
20x+12 | 20/8
20x
––––––
12

f(x)=3x/8 + 20/8 + 12/(8x), x ≠ 0, 2/3, or 8

f(x)=3x/8 + 5/2 + 3/(2x), x ≠ 0, 2/3, or 8

This is the simplest form; it shows a slant asymptote of y=3x/8 + 5/2.
Shelly J. | Excellent Maths Tutoring for academic successExcellent Maths Tutoring for academic su...
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Hi Theresa,

x²-2x-48=x²-8x+6x-48

=x(x-8)+6(x-8)
=(x+6)(x-8)

3x³-2x²=x²(3x-2)

9x³-4x=x(9x²-4)

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

8x-64=8(x-8)

so the given expression becomes,

(x+6)(x-8) × (x)(3x-2)(3x+2)
x²(3x-2)         8(x-8)

(x+6)(3x+2)
8x

For x=-6,-2/3 and 0 the solution is not defined.
Meena S. | Patient & knowledgeable Mathematics & Statistics (SPSS) TutorPatient & knowledgeable Mathematics & St...
4.5 4.5 (57 lesson ratings) (57)
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Hi Theresa,

factors of
x^2-2x-48=(x-8)(x+6)
3x^3-2x^2 = x^2(3x-2)
9x^3-4x = x(9x^2-4)= x(3x-2)(3x+2)
8x-64 = 8( x-8)

using all this factors,
(x-8)(x+6)  *  x(3x-2)(3x+2)
________      _____________
x^2(3x-2)      8(x-8)

=(x+6)(3x+2)
__________
8 x

=3x^2+20x+12
___________
8x

Meena from Strongsville,OH