Question

Divide the polynomial 12x2+2x−9 by 4x−2 . Then express the polynomial as the product of the divisor and the quotient plus the remainder. (1 point)
Responses

12x2+2x−9=(4x−2)(3x+2)+5
12 x squared plus 2 x minus 9 is equal to open paren 4 x minus 2 close paren times open paren 3 x plus 2 close paren plus 5

12x2+2x−9=(4x−2)(3x+2)−13
12 x squared plus 2 x minus 9 is equal to open paren 4 x minus 2 close paren times open paren 3 x plus 2 close paren minus 13

12x2+2x−9=(4x−2)(3x+2)−5
12 x squared plus 2 x minus 9 is equal to open paren 4 x minus 2 close paren times open paren 3 x plus 2 close paren minus 5

12x2+2x−9=(4x−2)(3x−1)−11

Answers

There are no human answers yet.
Answered by GPT-4o mini
To divide the polynomial \(12x^2 + 2x - 9\) by \(4x - 2\), we can use polynomial long division.

### Steps for Long Division:

1. **Divide the Leading Terms**:
\[
\frac{12x^2}{4x} = 3x
\]

2. **Multiply by the Divisor**:
\[
3x(4x - 2) = 12x^2 - 6x
\]

3. **Subtract**:
\[
(12x^2 + 2x - 9) - (12x^2 - 6x) = 8x - 9
\]

4. **Repeat the Process**:
- Divide the leading terms:
\[
\frac{8x}{4x} = 2
\]
- Multiply by the divisor:
\[
2(4x - 2) = 8x - 4
\]
- Subtract:
\[
(8x - 9) - (8x - 4) = -5
\]

Now we have a quotient of \(3x + 2\) and a remainder of \(-5\).

### Final Expression:
The polynomial can be expressed as:
\[
12x^2 + 2x - 9 = (4x - 2)(3x + 2) - 5
\]

So, the correct response is:
\[
12x^2 + 2x - 9 = (4x - 2)(3x + 2) - 5
\]