Question

Divide 2 x cubed minus 7 x squared plus 2 x plus 3 by x minus 3 using long division.
(1 point)
Responses

2 x squared minus 13 x plus 41 R negative 120
Image with alt text: 2 x squared minus 13 x plus 41 R Image with alt text: negative 120

8 x squared plus 17 x plus 53 R 162
Image with alt text: 8 x squared plus 17 x plus 53 R 162

2 x cubed plus 3 x plus 1
Image with alt text: 2 x cubed plus 3 x plus 1

2 x squared minus x minus 1
Image with alt text: 2 x squared minus x minus 1

Answer 1

To perform long division of \( 2x^3 - 7x^2 + 2x + 3 \) by \( x - 3 \), follow these steps:

1. Divide the leading term of the numerator \( 2x^3 \) by the leading term of the denominator \( x \):
\[
2x^3 \div x = 2x^2
\]

2. Multiply \( 2x^2 \) by \( x - 3 \) and subtract from the original polynomial:
\[
(2x^3 - 7x^2 + 2x + 3) - (2x^2 \cdot (x - 3)) = (2x^3 - 7x^2 + 2x + 3) - (2x^3 - 6x^2) = -1x^2 + 2x + 3
\]

3. The next term is \( -1x^2 \). Divide by \( x \):
\[
-1x^2 \div x = -1x
\]

4. Multiply \( -1x \) by \( x - 3 \) and subtract:
\[
(-x^2 + 2x + 3) - (-1x \cdot (x - 3)) = (-x^2 + 2x + 3) - (-x^2 + 3x) = -x + 3
\]

5. Divide \( -x \) by \( x \):
\[
-x \div x = -1
\]

6. Multiply \( -1 \) by \( x - 3 \) and subtract:
\[
(-x + 3) - (-1 \cdot (x - 3)) = (-x + 3) - (-x + 3) = 0
\]

So, there is no remainder, and the result from the division is:
\[
2x^2 - x - 1
\]

Thus, the answer is:
**2 x squared minus x minus 1**