Question

Two positive integers have a sum of 21 and a product of 108. what are the integers

Answer 1

X= first integer
21-x= second integer

(x)(21-x)= 108
multiply x by each term in parentheses

21x - x^2= 108
subtract 108 from both sides

21x - x^2 - 108= 0
-x^2 + 21x - 108= 0
multiply whole equation by -1 to eliminate the negative coefficient in the first term

(-1)(-x^2 + 21x - 108)= 0
x^2 - 21x + 108= 0
factor (remember we need #s to add to 21 and multiply to 108)

(x-12)(x-9)= 0

x-12= 0
x= 12

x-9= 0
x= 9

CHECK:
9 + 12= 21
9 * 12= 108

ANSWER: The two positive integers that add to 21 and multiply to 108 are 12 and 9.

Hope this helps! :)