Question

The equation

Answer 1

Answer:

a = -3

Explanation:

Using the leading terms of the polynomial and quotient, we can find the leading term of the divisor

24x²/ax = -8x

24x² = -8ax²

-8a = 24

a = 24/-8

a = -3

Answer 2

Answer:

B. -3

Explanation:

Our equation is: $\frac{24x^2+25x-47}{ax-2} =-8x-3-\frac{53}{ax-2}$ . We see that both sides have a term with denominator ax - 2, so let's add $\frac{53}{ax-2}$ to both sides:

$\frac{24x^2+25x-47}{ax-2} =-8x-3-\frac{53}{ax-2}$

$\frac{24x^2+25x-47}{ax-2}+\frac{53}{ax-2} =-8x-3$

$\frac{24x^2+25x+6}{ax-2}=-8x-3$

Now multiply both sides by ax - 2:

$24x^2+25x+6=(-8x-3)(ax-2)=-8ax^2-3ax+16x+6$

$24x^2+25x+6=(-8a)x^2+(16-3a)x+6$

We essentially want to make the terms on each side match. Look at the coefficient of x² on the left side: it's 24. That means on the right side, it should be 24, as well. Then, set -8a equal to 24:

-8a = 24

a = -3

Thus, the answer is B.