To simplify the expression \(-10x^2 + 20x + 80\) divided by \(x + 2\), we can follow these steps:
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Factor the numerator: First, we'll take the numerator \(-10x^2 + 20x + 80\) and factor it.
Factor out \(-10\): \[ -10(x^2 - 2x - 8) \]
Now, we need to factor \(x^2 - 2x - 8\). We look for two numbers that multiply to \(-8\) and add to \(-2\). The numbers that satisfy this are \(2\) and \(-4\). Thus, we can factor it as: \[ x^2 - 2x - 8 = (x - 4)(x + 2) \]
Therefore, the numerator can be rewritten as: \[ -10(x - 4)(x + 2) \]
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Rewrite the expression: The original expression can be rewritten now: \[ \frac{-10(x - 4)(x + 2)}{x + 2} \]
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Cancel out the common term: Since there's a common factor of \((x + 2)\) in both the numerator and the denominator, we can cancel it out (as long as \(x \neq -2\)): \[ -10(x - 4) \]
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Distribute: Finally, distribute \(-10\): \[ -10x + 40 \]
Thus, the simplified expression for \(-10x^2 + 20x + 80\) divided by \(x + 2\) is:
\[ -10x + 40 \]
From the given options, the answer is:
c. -10x + 40.