- WE WANT TO SOLVE EACH EQUATION  
BY FACTORING.
THE FIRST STEP IN FACTORING
IS TO FACTOR OUT 
THE GREATEST COMMON FACTOR.
LOOKING AT OUR FIRST EXAMPLE 
WE HAVE X SQUARED + 4X = 0.
NOTICE HOW THEY BOTH SHARE 
A COMMON FACTOR OF X,
WHICH IS THE GREATEST COMMON 
FACTOR.
SO IF WE FACTOR OUT X
WE WOULD HAVE X x THE QUANTITY, 
X + 4 = 0.
NOTICE X x X IS X SQUARED 
AND X x 4 IS = TO 4X.
AND NOW WE CAN USE 
THE ZERO PRODUCT PROPERTY
TO SOLVE THIS EQUATION;
MEANING IF WE HAVE 
X x THE QUANTITY, X + 4 = 0,
EITHER THE FIRST FACTOR 
OF X MUST = 0
OR THE FACTOR OF X + 4 MUST = 0.
WELL, THIS EQUATION 
IS ALREADY SOLVED FOR X,
BUT FOR THE SECOND EQUATION
WE'LL HAVE TO SUBTRACT 
4 ON BOTH SIDES
AND WE HAVE X = -4.
SO OUR SOLUTIONS 
ARE X = 0 OR X = -4.
LOOKING AT OUR SECOND EQUATION
WE ALWAYS WANT TO START
BY LOOKING 
FOR THE GREATEST COMMON FACTOR.
SO WE HAVE 14 X SQUARED - 35X.
HERE THE GREATEST COMMON FACTOR 
WOULD BE 7X
SINCE WE CAN WRITE 14X SQUARED 
AS 2 x 7 x X x X
AND 35 WOULD BE 5 x 7 x X.
NOTICE BOTH TERMS HAVE A FACTOR 
OF 7 AS WELL AS A FACTOR OF X.
SO IN FACTORED FORM WE WOULD 
HAVE 7X x THE QUANTITY
2X - 5 = 0.
AND NOW USING THE ZERO PRODUCT 
PROPERTY
WE HAVE 7X x THE QUANTITY 
2X - 5 = 0.
SO EITHER 7X = 0 OR 2X - 5 = 0.
OVER HERE WE COULD DIVIDE 
BOTH SIDES BY 7,
BUT WE'RE STILL 
GOING TO HAVE X = 0.
OVER HERE WE'D ADD 5 
TO BOTH SIDES,
THAT WOULD GIVE US 2X = 5 
AND DIVIDE BOTH SIDES BY 2
SO WE HAVE X = 5 HALVES.
SO OUR SOLUTIONS ARE X = 0 
OR X = 5 HALVES.
SO IT IS IMPORTANT TO REMEMBER 
WHENEVER FACTORING,
THE FIRST STEP IS TO FACTOR OUT 
THE GREATEST COMMON FACTOR.
I HOPE 
YOU FOUND THIS HELPFUL.
