Question

What is the product of 2x - 5 and 3x² + 5x - 7? Write your answer in standard form.

(a) Show your work.
(b) Is the product of 2x - 5 and 3x² + 5x - 7 equal to the product of 5x - 2 and 3x² + 5x - 7? Explain your answer.​

Answer 1

see below

Explanation:

(a)

`( 2x - 5 )(3x^(2) + 5x - 7)\\\\=2x(3x^2+5x-7)-5(3x^2+5x-7)\\\\=6x^3+10x^2-14x-15x^2-25x+35\\\\=6x^3+(10x^2-15x^2)+(-14x-25x)+35\\\\=6x^3-5x^2-39x+35`

(b)

`(2x-5)(3x^2+5x-7)=(5x-2)(3x^2+5x-7)\\\\(1)/((3x^2+5x-7))(2x-5)(3x^2+5x-7)= (1)/((3x^2+5x-7))(5x-2)(3x^2+5x-7)\\\\2x-5=5x-2\\\\2x-5x=-2+5\\\\-3x=3\\\\x=-1`

only happens when x=-1, not always