SOLUTION: Factor completely: 1. x^3 - 26x^ + 48x 2. x^ - 6wy + 3xy -2 wx 3. x^2 -5x - 14 4. 4x^2 - 36y^

Algebra ->  Equations -> SOLUTION: Factor completely: 1. x^3 - 26x^ + 48x 2. x^ - 6wy + 3xy -2 wx 3. x^2 -5x - 14 4. 4x^2 - 36y^      Log On


   



Question 116128: Factor completely:
1. x^3 - 26x^ + 48x
2. x^ - 6wy + 3xy -2 wx
3. x^2 -5x - 14
4. 4x^2 - 36y^

Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
1. x%5E3+-+26x%5E2+%2B+48x+……notice that x is common in all three terms, factor it out
x%28x%5E2+-+26x+%2B+48%29+………replace -+26x with the two numbers that multiply to 48 and add to -26, which are: -2 and -24
x%28x%5E2+-+2x+-+24x+%2B+48%29+………group the first two terms together and the last two terms together
x%28%28x%5E2+-+2x%29+%2B%28+-+24x+%2B+48%29%29+………factor a 1x out of the first group and factor a -24 out of the second group
x%281x%28x+-+2%29+-24%28+x+-+2%29%29+………now we have a common term x+%96+2 we can combine the two terms
x%28x+-24%29%28+x+-+2%29+………this is your answer

2.
x%5E2+-+6wy+%2B+3xy+-2+wx+
%28x%5E2+%2B+3xy%29+%2B+%28+-2+wx-+6wy+%29+
x%28x%2B+3y%29+-2w+%28+x+%2B+3y+%29+……………. combine the common terms
x%28x+-2w%29+%28+x+%2B+3y+%29+…………….

3.
x%5E2+-5x+-+14+
x%5E2+-5x+-+14+……….replace -5x with the two numbers that multiply to -14 and add to -5, which are +2 and -7
x%5E2+%2B+2x+-7x+-+14+……….group the first two terms together and the last two terms together
%28x%5E2+%2B+2x%29%2B%28-7x+-+14%29+……….Factor a x out of the first group and factor a -7 out of the second group
x%28x+%2B+2%29-+7%28+x+%2B+2%29+………combine the common terms
x%28x+-+7%29+%28+x+%2B+2+%29+…………….


4.
4x%5E2+-+36y%5E2………..notice that you can write 4 as a 2%5E2 and 36as a 6%5E2
2%5E2%2Ax%5E2+-6%5E2%2Ay%5E2..............we can write 6%5E2 as 2%5E2%2A3%5E2
2%5E2%2Ax%5E2+-2%5E2%2A3%5E2%2Ay%5E2..............factor out common 2%5E2
2%5E2%28x%5E2+-3%5E2%2Ay%5E2%29.............
2%5E2%28x%5E2+-%283y%29%5E2%29.............notice the difference square numbers, apply rule for it
4%28x+-3y%29%28x%2B3y%29.............