Question

Simplify the expression (x^2+3x-28)/(x^2+10x+ 21). Show your work.
NOTE: Must show your factoring work using either the big X strategy covered in class, or the quadratic formula method. Must show how you get factors. Not just give me factors.

Answer 1

Answer:

(x-3) (x-7)

Step-by-step explanation:

The first term is,  x2  its coefficient is  1 .

The middle term is,  -10x  its coefficient is  -10 .

The last term, "the constant", is  +21  

Step-1 : Multiply the coefficient of the first term by the constant   1 • 21 = 21  

Step-2 : Find two factors of  21  whose sum equals the coefficient of the middle term, which is   -10 .

     -21    +    -1    =    -22  

     -7    +    -3    =    -10    That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -7  and  -3  

                    x2 - 7x - 3x - 21

Step-4 : Add up the first 2 terms, pulling out like factors :

                   x • (x-7)

             Add up the last 2 terms, pulling out common factors :

                   3 • (x-7)

Step-5 : Add up the four terms of step 4 :

                   (x-3)  •  (x-7)

            Which is the desired factorization