Factor the trinomial x^2 − 7x + 10 what is the factored form of the trinomial, and why? a. (x−2)(x−5). the product of –2 and –5 is –10, and their sum is 7. b. (x−2)(x−5). the product of –2 and –5 is 10, and their sum is –7. c. (x+2)(x+5). the product of 2 and 5 is 10, and their sum is 7. d. (x+2)(x+5). the product of 2 and 5 is 10, and their sum is –7.

Lets get started :)

x² - 7x + 10

We are going to find something in this form:
                            ↓
           (                )(                )

x² is nothing but x multiplied by itself 
                            ↓
          (x               )(x               )             

-7x + 10 follows
since the sum is negative and the product is positive then the signs inside the bracket will be as follows
                         ↓
              ( x  -    )( x  -   )

-7x should be the sum and 10 should be the product
multiples of 10 = 1 x 10       =       2 x 5      =    -1 x -10     =   -2 x -5          
                               ↓                       ↓                   ↓                   ↓
                          1 + 10 = 11          2 + 5 = 7      -1 - 10 = -11    = -2 -5 = -7  

So the sum of -2 and -5 is -7 and the product of -2 and -5 is 10
                                            ↓
                                 ( x - 2 )( x - 5 )

Your final answer will be option B