The equation 24x2+25x−47a/x−2 = −8x − 3 − 53/ax−2 is true for all values of x≠ 2/a, where a is a constant.

What is the value of a?

A) -16
B) -3
C) 3
D) 16

B.) -3

Step-by-step explanation:

There are two ways to solve this question. The faster way is to multiply each side of the given equation by ax−2 (so you can get rid of the fraction). When you multiply each side by ax−2, you should have:

24x2+25x−47=(−8x−3)(ax−2)−53

You should then multiply (−8x−3) and (ax−2) using FOIL.

24x2+25x−47=−8ax2−3ax+16x+6−53

Then, reduce on the right side of the equation

24x2+25x−47=−8ax2−3ax+16x−47

Since the coefficients of the x2-term have to be equal on both sides of the equation, −8a=24, or a=−3.

Therefore, B.) -3

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B) a = -3

Step-by-step explanation:

You can find the leading term of the divisor using the leading terms if the polynomial and the quotient

24x²/ax = -8x

ax = 24/(-8x)

ax = -3x

a = -3

horizontal translation of 2 units in the positive x direction

followed by

vertical translation of 3 units in the positive y direction

step-by-step explanation:

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