Algebra
posted by Acezar on .
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?

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 
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 
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)