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

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