Question

Find the product of (x^2 - 3x + 5) with the quotient of (10x^6 - 15x^5 - 5x^3) ÷ 5x^3.

I need some help with this. I'm really unclear on the steps and how to solve this as a whole. I don't just need an answer, I'd like to know the steps as well. Please?

Answer 1

Nevermind, I figured it out:

The quotient:
(10x^6 - 15x^5 - 5x^3)/(5x^3 )
(10x^6)/(5x^3 ) - (15x^5)/(5x^3 ) - (5x^3)/(5x^3 )
2x3 - (15x^5)/(5x^3 ) - (5x^3)/(5x^3 )
2x3 - 3x2 - (5x^3)/(5x^3 )
2x3 - 3x2 - 1

The product using the quotient:
(x2 - 3x + 5)(2x3 - 3x2 - 1)
x2 ∙ 2x3 + x2 ∙ -3x2 + x2 ∙ - 1 - 3x ∙ 2x3 - 3x ∙ -3x2 - 3x ∙ -1 + 5 ∙ 2x3 + 5 ∙ -3x2 + 5 ∙ -1
2x5 - 9x4 + 19x3 - 16x2 + 3x - 5

Answer 2

Here's a better format. Good luck to anyone else who has this problem.

The quotient:
(10x^6 - 15x^5 - 5x^3)/(5x^3 )
(10x^6)/(5x^3 ) - (15x^5)/(5x^3 ) - (5x^3)/(5x^3 )
2x^3 - (15x^5)/(5x^3 ) - (5x^3)/(5x^3 )
2x^3 - 3x^2 - (5x^3)/(5x^3 )
2x^3 - 3x^2 - 1

The product using the quotient:
(x^2 - 3x + 5)(2x^3 - 3x^2 - 1)
x^2 * 2x^3 + x^2 * -3x^2 + x^2 * - 1 - 3x * 2x^3 - 3x * -3x^2 - 3x * -1 + 5 * 2x^3 + 5 * -3x^2 + 5 * -1
2x^5 - 9x^4 + 19x^3 - 16x^2 + 3x - 5

Answer 3

The idea is to solve the quotient first, by dividing each term by 5x^3.

Once the solution is found: 2x^3 - 3x^2 - 1

Then use that quotient and multiply it by (x^2 - 3x + 5).

Thus: (x^2 - 3x + 5)(2x^3 - 3x^2 - 1)