Question

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

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

Answer 1

The correct option is B 1 or -11

As x is an integer.

Therefore,

x+2, x+4, x+6 and x+8 are four consecutive odd/even integers.

Their product = 945, which is odd.

Therefore, x+2, x+4, x+6 and x+8 must be odd.

Factorising 945 as a product of 4 consecutive odd integers.

$945=3\left(5\right)\left(7\right)\left(9\right)=(-3)(-5)(-7)(-9)$

The smallest, i.e., $x+2=3$ or $-9$

Therefore, $x=1$ or $x=-11$