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Factor completely. Select "Prime" if the polynomial cannot be factored. \( -12-t+t^{2} \) \( -12-t+t^{2}=\square \)

Ask by Watkins Flynn. in the United States
Mar 12,2025

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\( -12 - t + t^{2} = -(4 - t)(3 + t) \)

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The Deep Dive

To factor the polynomial \( -12 - t + t^2 \), first, let's rearrange it into standard form: \( t^2 - t - 12 \). Now, we need two numbers that multiply to -12 (the constant term) and add to -1 (the coefficient of the \( t \) term). The numbers -4 and 3 fit the bill perfectly! Therefore, we can factor it as \( (t - 4)(t + 3) \). So, \( -12 - t + t^2 = (t - 4)(t + 3) \). Time to plug in those numbers and celebrate the factored form!

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