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Divide. If the polynomial does not divide evenly, include the remainder as a fraction. (-16g^3 - 62g^2 +...

Divide. If the polynomial does not divide evenly, include the remainder as a fraction.
(-16g^3 - 62g^2 + 8g) ÷ (g + 4)

Answer

To divide the polynomial, use synthetic or long division. Here, we'll use synthetic division:

Set up the synthetic division with the zero of the divisor, which is -4.
Write the coefficients of the dividend: -16, -62, 8.
Bring down the first coefficient: -16.
Multiply -16 by -4 and add to the next coefficient: (-16 * -4) + (-62) = 2.
Multiply 2 by -4 and add to the next coefficient: (2 * -4) + 8 = 0.

The quotient is -16g^2 + 2g, and the remainder is 0. Therefore, the division is exact, and the result is:

-16g^2 + 2g

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