Factor the trinomial 2x^2+5x+2

To factor the trinomial 2x^2 + 5x + 2, we are looking for two binomials in the form (ax + b)(cx + d) that multiply to give us the original trinomial.

The first term of each binomial will always be x since we are factoring a quadratic trinomial. So we have (x + _)(x + _).

The last term of each binomial will have to multiply to give 2 since 2 is the constant term in our original trinomial. The only possible options are 1 and 2 itself.

Next, we look at the middle term of the trinomial, which is 5x. The only way to get 5x is to multiply the first term of the first binomial (x) by 2 and the second term of the second binomial (also x) by 1. Therefore, we know that our binomials will be (x + 1)(2x + 2).

Multiplying these binomials out gives us:

(x + 1)(2x + 2)
= x(2x) + x(2) + 1(2x) + 1(2)
= 2x^2 + 2x + 2x + 2
= 2x^2 + 4x + 2

So, the factored form of the trinomial 2x^2 + 5x + 2 is (x + 1)(2x + 2).