Factor the trinomial: -x^2 - 3x + 28
Understand the Problem
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Answer
$-(x+7)(x-4)$
Answer for screen readers
$-(x+7)(x-4)$
Steps to Solve
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Factor out -1 Factor out $-1$ from the expression to make the leading coefficient positive: $$-x^2 - 3x + 28 = -(x^2 + 3x - 28)$$
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Factor the quadratic inside the parenthesis We need to find two numbers that multiply to $-28$ and add up to $3$. These numbers are $7$ and $-4$. Therefore, we can factor the quadratic as: $$x^2 + 3x - 28 = (x + 7)(x - 4)$$
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Write the final factored form Substitute the factored form back into the expression with the $-1$ factored out: $$-(x^2 + 3x - 28) = -(x + 7)(x - 4)$$
$-(x+7)(x-4)$
More Information
The factored form of the quadratic expression $-x^2 - 3x + 28$ is $-(x+7)(x-4)$.
Tips
A common mistake is forgetting to factor out the $-1$ at the beginning, which can lead to incorrect factoring. Also, errors in finding the correct factors of the constant term can occur.
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