Question

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

Answer 1

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

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)`