Step-by-step explanation: When first looking this problem, you will probably want to to factor out a greatest common factor.
The problem is that there is no factor that is common between these 3 terms so you might think that this problem is unfactorable.
However, the trinomial that you see is in a special form that can be factored in a new way. The first term has an X², the second term has an X, and the third term is a constant term.
When a trinomial is in this form, it can be factored as the product of two binomials. In other words, we are going to set up two sets of parentheses and within each set of parentheses we will have the two terms that compose each binomial.
The first term in each binomial will be a factor of the X². Since X² factors as X multiplied by X, we can use X as the first term in each binomial. The second term in each binomial will be a factor of your constant term or your 10.
However, 10 factors in different ways. 10 can be thought of as 10 × 1 or it can also be thought of as 5 × 2. To decide which one we should use, take a look at your middle term in your original polynomial. The rule is that the factors of the last term that you will use have to add to the middle term in the original trinomial.
Since 5 and 2 add to 7, we put a 5 in our first binomial and a 2 in our second binomial.
Now we have (x + 5)(x + 2) which is our answer.
