Question

Factorise $x^2+5x+6$ by using the Factor Theorem.

• A. $(x+2)(x+3)$
• B. $(x+2)(x+6)$
• C. $(x+5)(x+3)$
• D. $(x+2)(x+4)$

Answer 1

The correct option is A

$(x+2)(x+3)$

Let $p\left(x\right)=x^2+5x+6$.

Let factors be $(x-a)and(x-b)$

So, $p\left(x\right)=(x–a)(x–b)$

$\Rightarrow p\left(x\right)=x^2–bx–ax+ab$

On comparing the constants, we get ab = 6.

The factors of 6 are -1,1, 2,-2,-3 and 3.

Now, $p(-2)=(-2{)}^2+(5\times (-2))+6=4–10+6=0$.

So, (x +2) is a factor of p(x).

Also, $p(-3)=(-3{)}^2+(5\times (-3))+6=9–15+6=0$

So, (x + 3) is also a factor of p(x).

Therefore, $x^2+5x+6=(x+2)(x+3)$