SOLUTION: What are three different values for the expression x^2 + ______x +24 so that you can factor it into the product of two binomials?

Algebra ->  Customizable Word Problem Solvers  -> Misc -> SOLUTION: What are three different values for the expression x^2 + ______x +24 so that you can factor it into the product of two binomials?      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1176238: What are three different values for the expression x^2 + ______x +24 so that you can factor it into the product of two binomials?
Found 3 solutions by Alan3354, MathLover1, ikleyn:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
What are three different values for the expression x^2 + ______x +24 so that you can factor it into the product of two binomials?
-------------
10
-10
25
-25
14
-14
11
-11

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!


To factor a trinomial in the form x%5E2+%2B+bx+%2B+c, find two integers, r and s, whose product is c and whose sum is b.
x%5E2+%2B+bx+%2B24
c=24
rs=c
rs=24......eq.1
1.
24=3%2A8
r=3
s=8
r%2Bs=b=11
x%5E2+%2B+11x+%2B24
x%5E2+%2B+3x%2B8x+%2B24
%28x%5E2+%2B+3x%29%2B%288x+%2B24%29
x%28x%2B+3%29%2B8%28x+%2B3%29
%28x%2B8%29%28x+%2B3%29
2.
24=2%2A12
r=2
s=12
r%2Bs=14
x%5E2+%2B+14x+%2B24
x%5E2+%2B+2x%2B12x+%2B24
%28x%5E2+%2B+2x%29%2B%2812x+%2B24%29
x%28x%2B+2%29%2B12%28x+%2B2%29
%28x%2B2%29%28x+%2B12%29
3.
24=4%2A6
r=4
s=6
r%2Bs=10
x%5E2+%2B+10x+%2B24
x%5E2+%2B+4x%2B6x+%2B24
%28x%5E2+%2B+4x%29%2B%286x+%2B24%29
x%28x%2B+4%29%2B6%28x+%2B4%29
%28x%2B4%29%28x+%2B6%29


Answer by ikleyn(52776) About Me  (Show Source):
You can put this solution on YOUR website!
.

There are 4 different decompositions of the number 24 into the product 


    24 = 24*1

    24 = 12*2

    24 =  8*3

    24 =  6*4


Accordingly, there are 8 integer values  

    25, -25;  

    14, -14;  

    11, -11;

    10, -10

as coefficients at x,  providing decomposition of the given trinomial into the product of linear binomials with integer coefficients.