Question

assignment 5.4 dividing polynomials
due friday by 11:59pm points 9 submitting an external tool
assignment 5.4 dividing polynomials
score: 2/9 answered: 2/9
question 3
find the quotient and remainder using polynomial long division.
\\(\frac{-5x^{4}+15x^{3}-24x^{2}-4x + 4}{5x^{2}-1}\\)
the quotient is
the remainder is
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Explanation:

Step1: Divide leading terms

Divide the leading - term of the numerator $-5x^{4}$ by the leading - term of the denominator $5x^{2}$. $\frac{-5x^{4}}{5x^{2}}=-x^{2}$. This is the first term of the quotient.

Step2: Multiply and subtract

Multiply the denominator $5x^{2}-1$ by $-x^{2}$ to get $-5x^{4}+x^{2}$. Subtract this from the numerator $(-5x^{4}+15x^{3}-24x^{2}-4x + 4)-(-5x^{4}+x^{2})=15x^{3}-25x^{2}-4x + 4$.

Step3: Divide leading terms again

Divide the leading - term of the new numerator $15x^{3}$ by the leading - term of the denominator $5x^{2}$. $\frac{15x^{3}}{5x^{2}} = 3x$. This is the second term of the quotient.

Step4: Multiply and subtract again

Multiply the denominator $5x^{2}-1$ by $3x$ to get $15x^{3}-3x$. Subtract this from the new numerator $(15x^{3}-25x^{2}-4x + 4)-(15x^{3}-3x)=-25x^{2}-x + 4$.

Step5: Divide leading terms one more time

Divide the leading - term of the new numerator $-25x^{2}$ by the leading - term of the denominator $5x^{2}$. $\frac{-25x^{2}}{5x^{2}}=-5$. This is the third term of the quotient.

Step6: Multiply and subtract for the last time

Multiply the denominator $5x^{2}-1$ by $-5$ to get $-25x^{2}+5$. Subtract this from the new numerator $(-25x^{2}-x + 4)-(-25x^{2}+5)=-x - 1$.

Answer:

The quotient is $-x^{2}+3x - 5$
The remainder is $-x - 1$