SOLUTION: Use the ac test to determine which of the following trinomials can be factored. Find the values of m and n for each trinomial that can be factored. x(squared) + 2x - 15 tha

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Use the ac test to determine which of the following trinomials can be factored. Find the values of m and n for each trinomial that can be factored. x(squared) + 2x - 15 tha      Log On


   

Question 76274: Use the ac test to determine which of the following trinomials can be factored. Find the values of m and n for each trinomial that can be factored.
x(squared) + 2x - 15

thanks
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Solved by pluggable solver: Factoring Quadratics with a leading coefficient of 1 (a=1)
In order to factor 1%2Ax%5E2%2B2%2Ax%2B-15, first we need to ask ourselves: What two numbers multiply to -15 and add to 2? Lets find out by listing all of the possible factors of -15


Factors:

1,3,5,15,

-1,-3,-5,-15,List the negative factors as well. This will allow us to find all possible combinations

These factors pair up to multiply to -15.

(-1)*(15)=-15

(-3)*(5)=-15

Now which of these pairs add to 2? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 2

||||
First Number|Second Number|Sum
1|-15|1+(-15)=-14
3|-5|3+(-5)=-2
-1|15|(-1)+15=14
-3|5|(-3)+5=2
We can see from the table that -3 and 5 add to 2.So the two numbers that multiply to -15 and add to 2 are: -3 and 5 Now we substitute these numbers into a and b of the general equation of a product of linear factors which is: %28x%2Ba%29%28x%2Bb%29substitute a=-3 and b=5 So the equation becomes: (x-3)(x+5) Notice that if we foil (x-3)(x+5) we get the quadratic 1%2Ax%5E2%2B2%2Ax%2B-15 again


So our polynomial factors to
%28x-3%29%28x%2B5%29
Notice %28x-3%29%28x%2B5%29 foils back to x%5E2%2B2x-15