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Divide.

[tex]\[
\left(20x^4 - 12x^3 + 10x^2 + 3x - 16\right) \div \left(-4x^2 + 2\right)
\][/tex]

Write your answer in the following form: Quotient \( + \frac{\text{Remainder}}{-4x^2 + 2} \)

[tex]\[
\frac{20x^4 - 12x^3 + 10x^2 + 3x - 16}{-4x^2 + 2} = \square + \frac{\square}{-4x^2 + 2}
\][/tex]

Sagot :

GinnyAnswer
To divide the polynomial \( 20x^4 - 12x^3 + 10x^2 + 3x - 16 \) by \( -4x^2 + 2 \), we proceed with polynomial division.

Given the result of the division, the quotient is:
[tex]\[ -5x^2 + 3x - 5 \][/tex]

And the remainder is:
[tex]\[ -3x - 6 \][/tex]

Thus, the division expression can be written as:
[tex]\[ \frac{20x^4 - 12x^3 + 10x^2 + 3x - 16}{-4x^2 + 2} = -5x^2 + 3x - 5 + \frac{-3x - 6}{-4x^2 + 2} \][/tex]

So, our final result in the required form is:
[tex]\[ \boxed{-5x^2 + 3x - 5 + \frac{-3x - 6}{-4x^2 + 2}} \][/tex]
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