Question

divide. if the polynomial does not divide evenly, include the remainder as a fraction.\\((y^3 - 100y) \div (y - 10)\\)

Explanation:

Step1: Factor the dividend

First, factor out the common term $y$ from the dividend:
$y^3 - 100y = y(y^2 - 100)$
Then factor the difference of squares $y^2 - 100$:
$y(y^2 - 100) = y(y - 10)(y + 10)$

Step2: Cancel common factors

Divide the factored dividend by the divisor $(y - 10)$, cancel the common factor:
$\frac{y(y - 10)(y + 10)}{y - 10} = y(y + 10)$

Step3: Expand the result

Distribute $y$ to simplify the expression:
$y(y + 10) = y^2 + 10y$

Answer:

$y^2 + 10y$