Question

The number that is to be added to $4x^2+24x+32$ to make the resultant a perfect square is ______.

• A. 2
• B. 4
• C. 6
• D. 8

Answer 1

The correct option is B 4

Given equation is $4x^2+24x+32$

Taking 4 as common

= 4($x^2+6x+8)$

= <!--td {border: 1px solid #ccc;}br {mso-data-placement:same-cell;}--> $2^2(x^2+2\times 3\times x+8)$

Adding and subtracting $3^2$

= $2^2(x^2+2\times 3\times x+3^2-3^2+8)$

= $2^2\left[\right(x+3{)}^2-9+8]$

= $2^2\left[\right({x+3)}^2-1]$

=$2^2({x+3)}^2-2^2$

=$\left[2\right(x+3){]}^2-4$

It will be a perfect square, if we add 4 to it.