Question

factor the expression.
$-y^{3}+y^{2}+30y$
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hint: to add an exponent ($x^y$), type \exponent\ or press \^\
enter your answer

factor the expression.
$-s^{3}-6s^{2}+16s$
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hint: to add an exponent ($x^y$), type \exponent\ or press \^\
enter your answer

Explanation:

First Expression: $-y^3 + y^2 + 30y$

Step1: Factor out -y

First, we can factor out a common factor of $-y$ from each term.
$$-y^3 + y^2 + 30y = -y(y^2 - y - 30)$$

Step2: Factor the quadratic

Now, we need to factor the quadratic $y^2 - y - 30$. We look for two numbers that multiply to $-30$ and add up to $-1$. The numbers are $-6$ and $5$ because $(-6) \times 5 = -30$ and $-6 + 5 = -1$. So we can factor the quadratic as:
$$y^2 - y - 30 = (y - 6)(y + 5)$$

Step3: Combine the factors

Putting it all together, we have:
$$-y^3 + y^2 + 30y = -y(y - 6)(y + 5)$$

Step1: Factor out -s

First, factor out a common factor of $-s$ from each term.
$$-s^3 - 6s^2 + 16s = -s(s^2 + 6s - 16)$$

Step2: Factor the quadratic

Now, factor the quadratic $s^2 + 6s - 16$. We look for two numbers that multiply to $-16$ and add up to $6$. The numbers are $8$ and $-2$ because $8 \times (-2) = -16$ and $8 + (-2) = 6$. So we can factor the quadratic as:
$$s^2 + 6s - 16 = (s + 8)(s - 2)$$

Step3: Combine the factors

Putting it all together, we have:
$$-s^3 - 6s^2 + 16s = -s(s + 8)(s - 2)$$

Answer:

$-y(y - 6)(y + 5)$

Second Expression: $-s^3 - 6s^2 + 16s$