Answer:
A)What is the product of 2x -5 and 3x^2 + 5x - 7? Write your answer in standard form.
6x³ - 5x² - 39x + 35 = 0
B. Is the product of 2x -5 and 3x^2 + 5x -7 equal to the product of 5x - 2 and 3x^2 + 5x - 7?
No it is not.
Explanation:
A)What is the product of 2x -5 and 3x^2 + 5x - 7? Write your answer in standard form.
(2x - 5) (3x² + 5x - 7)
= 2x(3x² + 5x - 7) -5(3x² + 5x - 7)
= 6x³ + 10x² - 14x -15x² - 25x +35
Collecting like terms
= 6x³ +10x² - 15x² - 14x - 25x +35
= 6x³ - 5x² - 39x + 35
In standard form
6x³ - 5x² - 39x + 35 = 0
B. Is the product of 2x -5 and 3x^2 + 5x -7 equal to the product of 5x - 2 and 3x^2 + 5x - 7?
First we find the product of
5x - 2 and 3x² + 5x - 7?
(5x - 2) (3x² + 5x - 7)
5x(3x² + 5x - 7) -2(3x² + 5x - 7)
15x³ + 25x² - 35x - 6x² -10x + 14
Collect like terms
15x³+ 25x² - 6x² -35x - 10x + 14
15x³ + 19x² - 45x + 14 = 0
Hence, the product of 5x - 2 and 3x^2 + 5x - 7
= 15x³ + 19x² - 45x + 14 = 0
The product of 2x -5 and 3x^2 + 5x -7 = 6x³ - 5x² - 39x + 35 = 0
Comparing both products, we can see that
The product of 2x -5 and 3x^2 + 5x -7 ≠ the product of 5x - 2 and 3x^2 + 5x - 7