Question

(4x+7)²/x+5 is integer. How many valur of x are possible

Answer 1

only one value is possible

Answer 2

Answer:

6

Step-by-step explanation:

To see this, carry out the division to express the ratio as P(x) + R(x)/(x+5).

Notice, I suspect the "x+5" was meant to be the denominator, so the expression in the question ought to be (4x+7)² / (x+5).  Also, I suspect that x is meant to be supposed to be an integer as well.

Doing this, we have

(4x + 7)² / (x + 5)

= (16x² + 56x + 49) / (x + 5)

= ( 16x(x+5) - 24x + 49 ) / (x + 5)

= ( 16x(x+5) -24(x+5) + 169 ) / (x + 5)

= 16x - 24 + 169 / (x+5).

Now for an integer x, this is an integer precisely when 169 / (x+5) is an integer.  The divisors of 169 are -169, -13, -1, 1, 13 and 169, so the original expression is an integer when x+5 takes these values, or in other words, when x = -174, -18, -6, -4, 8 and 164.