Question 8
Find the quotient and remainder using long division for

The quotient is
The remainder is
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Ask by Grant Simmons. in the United States

Mar 30,2025

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Question 8 Find the quotient and remainder using long division for $$ \frac{2 x^{3}-6 x^{2}+7 x-10}{2 x^{2}+5} $$ The quotient is The remainder is Question Help: Video D Post to forum Submit Question

UpStudy AI · Accepted Answer

1. Divide the leading term of the dividend by the leading term of the divisor:
   $$
   \frac{2x^3}{2x^2} = x.
   $$
   Multiply the divisor by $$ x $$:
   $$
   x(2x^2+5) = 2x^3+5x.
   $$

2. Subtract this product from the dividend:
   $$
   (2x^3-6x^2+7x-10) - (2x^3+5x) = -6x^2+2x-10.
   $$

3. Divide the new leading term by the leading term of the divisor:
   $$
   \frac{-6x^2}{2x^2} = -3.
   $$
   Multiply the divisor by $$-3$$:
   $$
   -3(2x^2+5) = -6x^2-15.
   $$

4. Subtract this product:
   $$
   (-6x^2+2x-10) - (-6x^2-15) = 2x+5.
   $$
   
The division yields:

- Quotient: $$ x-3 $$.
- Remainder: $$ 2x+5 $$.
The quotient is $$ x - 3 $$ and the remainder is $$ 2x + 5 $$.

Question 8
Find the quotient and remainder using long division for

The quotient is
The remainder is
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Question 8 Find the quotient and remainder using long division for The quotient is The remainder is Question Help: Video D Post to forum Submit Question