Question

Which of the following worked equations demonstrates that you can divide polynomials by recognizing division as the inverse operation of multiplication?

a) (x+2)(x-2) = x² - 4
b) (x² - 4) / (x+2) = x-2
c) x² - 4 = (x+2)(x-2)
d) (x-2) / (x+2) = 1

Answer 1

The worked equation that demonstrates dividing polynomials by recognizing division as the inverse operation of multiplication is (c) x² - 4 = (x+2)(x-2).

Step-by-step explanation:

The worked equation that demonstrates dividing polynomials by recognizing division as the inverse operation of multiplication is (c) x² - 4 = (x+2)(x-2). To divide polynomials, we can factorize the polynomial expression on the right side of the equation and simplify it to get the quotient on the left side of the equation. In this case, we recognize that (x+2)(x-2) is a difference of squares, which simplifies to x² - 4, resulting in the equation x² - 4 = (x+2)(x-2).