Tracey divided the two polynomials shown bel (24x^2+26x-33)/(4x+3) What is the quotient? 6x+11 6x-11 6x+2+(-39)/(4x+3) 6x+2+(-27)/(4x+3)

To find the quotient of the given polynomial division, we can use polynomial long division.<br /><br />Step 1: Divide the first term of the numerator by the first term of the denominator.<br />$\frac{24x^2}{4x} = 6x$<br /><br />Step 2: Multiply the entire denominator by the result from step 1 and subtract it from the numerator.<br />$(4x+3) \cdot 6x = 24x^2 + 18x$<br />$24x^2 + 26x - 33 - (24x^2 + 18x) = 8x - 33$<br /><br />Step 3: Repeat the process with the new numerator.<br />$\frac{8x}{4x} = 2$<br /><br />Step 4: Multiply the entire denominator by the result from step 3 and subtract it from the new numerator.<br />$(4x+3) \cdot 2 = 8x + 6$<br />$8x - 33 - (8x + 6) = -39$<br /><br />So, the quotient is $6x + 2 + \frac{-39}{4x+3}$.<br /><br />Therefore, the correct answer is $6x+2+\frac{-39}{4x+3}$.