SOLUTION: I need to factor 25w^2 - 121 completely. Thanks so much for your help.

Algebra.Com
Question 260820: I need to factor 25w^2 - 121 completely.

Thanks so much for your help.

Found 2 solutions by Theo, richwmiller:
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
set 25w^2 - 121 = 0 to find the roots.

add 121 to both sides of the equation to get:

25w^2 = 121

divide both sides by 25 to get:

w^2 = 121/25

take the square root of both sides to get:

w = +/- sqrt(121)/sqrt(25)

sqrt(121) = 11
sqrt(25) = 5

equation becomes:

w = +/- 11/5

graph of this equation looks like this:



you can see that y = 0 when x = +/- 11/5 which is equivalent to +/- 2.2

note:

to graph the equation, I substituted x for w to satisfy the graphing software requirements.


Answer by richwmiller(17219)   (Show Source): You can put this solution on YOUR website!
Here is how to factor it
Solved by pluggable solver: Factoring using the AC method (Factor by Grouping)


Looking at the expression , we can see that the first coefficient is , the second coefficient is , and the last term is .



Now multiply the first coefficient by the last term to get .



Now the question is: what two whole numbers multiply to (the previous product) and add to the second coefficient ?



To find these two numbers, we need to list all of the factors of (the previous product).



Factors of :

1,5,11,25,55,121,275,605,3025

-1,-5,-11,-25,-55,-121,-275,-605,-3025



Note: list the negative of each factor. This will allow us to find all possible combinations.



These factors pair up and multiply to .

1*(-3025) = -3025
5*(-605) = -3025
11*(-275) = -3025
25*(-121) = -3025
55*(-55) = -3025
(-1)*(3025) = -3025
(-5)*(605) = -3025
(-11)*(275) = -3025
(-25)*(121) = -3025
(-55)*(55) = -3025


Now let's add up each pair of factors to see if one pair adds to the middle coefficient :



First NumberSecond NumberSum
1-30251+(-3025)=-3024
5-6055+(-605)=-600
11-27511+(-275)=-264
25-12125+(-121)=-96
55-5555+(-55)=0
-13025-1+3025=3024
-5605-5+605=600
-11275-11+275=264
-25121-25+121=96
-5555-55+55=0




From the table, we can see that the two numbers and add to (the middle coefficient).



So the two numbers and both multiply to and add to



Now replace the middle term with . Remember, and add to . So this shows us that .



Replace the second term with .



Group the terms into two pairs.



Factor out the GCF from the first group.



Factor out from the second group. The goal of this step is to make the terms in the second parenthesis equal to the terms in the first parenthesis.



Combine like terms. Or factor out the common term



===============================================================



Answer:



So factors to .



In other words, .



Note: you can check the answer by expanding to get or by graphing the original expression and the answer (the two graphs should be identical).
RELATED QUESTIONS

I need to factor 24-11w+w^2= ? Thanks so much for your help. (answered by checkley77)
25w^2 - 25w = -3 I need help (answered by JBarnum)
Hi, I need help please. (0.4y^2-0.0025)Factor completely. Thanks so much, (answered by KMST)
I need to factor the polynomial completely 7. y^5-3y^3-9y^2+27 Thanks very much for (answered by josmiceli)
I need to factor the polynomial completely. 6. a^3-2a^2+5a-10 Thank you so much in (answered by jim_thompson5910)
Factor completely. 25w^2 + 16 - 40w I haven't done these type of problems for a... (answered by jim_thompson5910)
On my homework i would need to factor the polynomials completely; and that some... (answered by rapaljer)
Thanks so very much! I need your help! factor the quadratic expression completely, and... (answered by narayaba)
Factor each polynomial completely. 6+15w^5 7x^2+x Thanks so much for your help in (answered by jim_thompson5910)