Question

Use long division to divide the polynomial 15x2+14x−8 by 3x+4 . What is the quotient?(1 point)
Responses

5x−2
5 x minus 2

5x+2
5 x plus 2

5x−2+163x+4
5 x minus 2 plus Start Fraction 16 over 3 x plus 4 End Fraction

5x+2−163x+4

Answer 1

To divide the polynomial \(15x^2 + 14x - 8\) by \(3x + 4\) using long division, we follow these steps:

1. **Setup the long division**: Write \(15x^2 + 14x - 8\) under the long division symbol and \(3x + 4\) outside.

2. **Divide the leading terms**: Divide the leading term of the dividend \(15x^2\) by the leading term of the divisor \(3x\):
\[
\frac{15x^2}{3x} = 5x
\]
This becomes the first term of the quotient.

3. **Multiply and subtract**: Multiply \(5x\) by the entire divisor \(3x + 4\):
\[
5x(3x + 4) = 15x^2 + 20x
\]
Now subtract this from the original polynomial:
\[
(15x^2 + 14x - 8) - (15x^2 + 20x) = 14x - 20x - 8 = -6x - 8
\]

4. **Repeat the process**: Now we need to divide \(-6x\) by the leading term \(3x\):
\[
\frac{-6x}{3x} = -2
\]
This is the next term of the quotient.

5. **Multiply and subtract again**: Multiply \(-2\) by the divisor \(3x + 4\):
\[
-2(3x + 4) = -6x - 8
\]
Now subtract this from \(-6x - 8\):
\[
(-6x - 8) - (-6x - 8) = 0
\]

Since there is no remainder left, the quotient is simply:
\[
5x - 2
\]

Thus, the answer is:

**5x - 2**