Question

How do you Factor the expression b2+3b+2

Answer 1

(b + 1)(b + 2)

Explanation:

Ask yourself: What are possible factors of the constant, 2? They are {1, 2}.

Do these factors, when added together, result in 3? Yes.

Thus,

b^2+3b+2 = (b + 1)(b + 2) = b^2 + 1b + 2b + 2

Answer 2

You can factor a polynomial by finding its roots: if
`x_0` is a solution of
`p(x)`, i.e.
`p(x_0)=0`, then
`p(x)` is divisible by
`(x-x_0)`.

You keep factoring the polynomial until the remaining factor has no more roots, and is thus irreducible.

In this case, we have

`b^2+3b+2=0 \iff b=(-3\pm√(9-8))/(2) = (-3\pm 1)/(2) \implies b_1 = -2,\ b_2 = -1`

So, the polynomial can be written as

`b^2+3b+2=(b+1)(b+2)`