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

(x-3) (x-7)

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