Question

The equation
24x2+25x−47
ax−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?

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Answer 1

Answer:

a = −3.

Explanation:

24x2+ 25x − 47 divided by ax − 2 is equal to  

−8x −3 with remainder −53,

it is true that (−8x − 3)(ax − 2) − 53 = 24x2 +25x −47.

(This can be seen by multiplying each side of the given equation by ax − 2).

This can be rewritten as −8ax2+ 16x − 3ax = 24x2+ 25x − 47.

Since  

the coefficients of the x2  

-term have to be equal on both sides of the equation,  

−8a = 24, or a = −3.

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Answer 2

Answer:

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