Question

Factor a trinomial of the form x^2+bx+c

Answer 1

Answer:

$\mathrm{Factor}\:x^2+5x+6:\quad \left(x+2\right)\left(x+3\right)$

Step-by-step explanation:

Let us assume the trinomial of the form $x^2+bx+c$

$x^2+5x+6$

Break the expression into the groups

$=\left(x^2+2x\right)+\left(3x+6\right)$

Factor out 'x' from $x^2+2x$

i.e.

$\:x^2+2x=x\left(x+2\right)$

Factor out '3' from 3x+6

i.e.

3x+6 = 3(x+2)

so the expression becomes

$\:x^2+2x=x\left(x+2\right)$

$\mathrm{Factor\:out\:common\:term\:}x+2$

$=\left(x+2\right)\left(x+3\right)$

Hence,

$\mathrm{Factor}\:x^2+5x+6:\quad \left(x+2\right)\left(x+3\right)$