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

2 Answers
Mar 13, 2018

(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.

Mar 13, 2018

(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)