Question

If $(x+2)(x+4)(x+6)(x+8)=945$ and $x$ is an integer, then find $x$.

• A. $-1$
• B. $1$
• C. $-11$
• D. B or C

Answer 1

Answer: (D)

B or C

$945=3\times 3\times 3\times 5\times 7=3\times 5\times 7\times 9$ -- (1)
So, if $(x+2)(x+4)(x+6)(x+8)=956$ -- (2)
Then comparing eqns 1 and 2, we get
$x+2=3$
$=>x=1$
As the other options are $-1,-11$ substituting $-1$, we notice that
$(-1+2)\times (-1+4)\times (-1+6)\times (-1+8)=1\times 3\times 5\times 7=105\ne 945$
And substituting $-11$ , we notice that
$(-11+2)\times (-11+4)\times (-11+6)\times (-11+8)=-9\times -7\times -5\times -3=945$
So both $1,-11$ are possible values of $x$