Question

What is the product?

StartFraction x squared minus 16 Over 2 x + 8 EndFraction times StartFraction x cubed minus 2 x squared + x Over x squared + 3 x minus 4 EndFraction

Answer 1

[x(x - 1)(x - 4)]/(2(x + 4))

Step-by-step explanation:

We want to find;

[(x² - 16)/(2x + 8)] * [(x³ - 2x² + x)/(x² + 3x - 4)]

Now,

x² - 16 can be factorized as;

(x + 4)(x - 4)

Also, 2x + 8 can be factorized as;

2(x + 4)

Also, (x³ - 2x² + x) can factorized as;

x[x² - 2x + 1] = x[(x - 1)(x - 1)]

Also,(x² + 3x - 4) can be factorized out as; (x - 1)(x + 4)

So plugging in these factorized forms into the equation in the question, we have;

[(x + 4)(x - 4)/(2(x + 4))] * [x[(x - 1)(x - 1)] /((x - 1)(x + 4))

This gives;

((x - 4)/2) * x(x - 1)/(x +4)

This gives;

[x(x - 1)(x - 4)]/(2(x + 4))

Explanation:

the answer above, your welcome

Answer 2

x^5-2x⁴-15x³+32x²-16x/2x³+14x²+16x-32

Explanation:

Given the mathematical operation

x²-16/2x+8 × x³-2x²+x/x²+3x-4

(x²-16)(x³-2x²+x)/(2x+8)(x²+3x-4)

On expanding the numerator and denominator we have;

x^5-2x⁴+x³-16x³+32x²-16x/2x³+6x²-8x+8x²+24x-32

= x^5-2x⁴-15x³+32x²-16x/2x³+14x²+16x-32