Question

How do you factor completely: `x^2 + 5x + 6`?

Answer 1

`(x + 3)(x + 2 )`

Explanation:

You need to first find 2 number which multiply to make 6 and add to make 5. It is easiest to list the factor pairs of 6:
`6 = 1 xx 6`
`6 = 2 xx 3`

`1 + 6 = 7`
`2 + 3 = 5`

Therefore we use the numbers 2 and 3. it doesnt matter which way round they go in the brackets.

Answer 2

`(x+2)(x+3)`, if `y=0`, `x=-2` or `-3`

Explanation:

First, we need to find factors of 6. The factors of 6 are 1,2,3, and 6.
Now see the function. `x^2+5x+6`. Because there is no substract operation,
`(x+a)(x+b) = x^2+5x+6`
`bx+ax=5x,` and `ab=6`
`x(b+a)=5x`, so `b+a=5`
`a+b=5` and `ab=6`.
Look at the factors. a must be 2 or 3, let's say a is 2, and b must be 3.
So: `(x+2)(x+3)=0`, (to find the factor)
`x+2=0, x=-2` ...(1)
`x+3=0, x=-3` ... (2)