Q. Divide. If there is a remainder, include it as a simplified fraction.(h3−3h2−10h)÷(h+2)______
Use Polynomial Long Division: To divide the polynomial (h3−3h2−10h) by the binomial (h+2), we will use polynomial long division.
Divide h3 by h: First, we divide the first term of the polynomial, h3, by the first term of the binomial, h, to get h2.
Multiply and Subtract: We then multiply the entire binomial (h+2) by h2 and subtract the result from the polynomial.(h+2)×h2=h3+2h2
Subtract and Divide: Subtracting this from the original polynomial gives us:(h3−3h2−10h)−(h3+2h2)=−5h2−10h
Multiply and Subtract: Next, we divide the first term of the new polynomial, −5h2, by the first term of the binomial, h, to get −5h.
Subtract and Complete: We then multiply the entire binomial (h+2) by −5h and subtract the result from the new polynomial.(h+2)×−5h=−5h2−10h
Subtract and Complete: We then multiply the entire binomial (h+2) by −5h and subtract the result from the new polynomial.(h+2)×−5h=−5h2−10hSubtracting this from the new polynomial gives us:(−5h2−10h)−(−5h2−10h)=0
Subtract and Complete: We then multiply the entire binomial (h+2) by −5h and subtract the result from the new polynomial.(h+2)⋅−5h=−5h2−10hSubtracting this from the new polynomial gives us:(−5h2−10h)−(−5h2−10h)=0Since we have no remainder, the division is complete.
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