Question

When two polynomials are subtracted the difference is -4x^2-7x+9. If one of the polynomials is x^2-4x+2, then determine the two possible options for the other polynomial.

Answer 1

The two options are:

-3x² - 11x + 11 and 5x² + 3x - 7

Explanation:

When two polynomials are subtracted the difference is

-4x² - 7x + 9

One of the polynomials is

x² - 4x + 2

To get the second polynomial, we an either add x² - 4x + 2 to -4x² - 7x + 9 or subtract -4x² - 7x + 9 from x² - 4x + 2

First Option:

(x² - 4x + 2) + (-4x² - 7x + 9)

= x² - 4x + 2 - 4x² - 7x + 9

= x² - 4x² - 4x - 7x + 2 + 9

= -3x² - 11x + 11

Secons Option:

(x² - 4x + 2) - (-4x² - 7x + 9)

= x² - 4x + 2 + 4x² + 7x - 9

= x² + 4x² - 4x + 7x + 2 - 9

= 5x² + 3x - 7

Therefore, the two options are:

-3x² - 11x + 11 and 5x² + 3x - 7