Question

$x^2+5x+6=$

• A. $(x+3)(x+5)$
• B. $(x+5{)}^2$
• C. $(x+3)(x+2)$

Answer 1

The correct option is C $(x+3)(x+2)$

Given: $x^2+5x+6.$
Comparing above expression with the identity $x^2+(a+b)x+ab$
We note that,$(a+b)=5\text{and}ab=6.$
$So,$
$(3+2)=5\text{and}\left(3\right)\left(2\right)=6$
Hence,
$x^2+5x+6$
$=x^2+3x+2x+6$
$=x(x+3)+2(x+3)$
$=(x+3)(x+2)$