Question 74044: Factor completely:
5x^2 – 38x – 16
Answer by checkley75(3666)   (Show Source):
You can put this solution on YOUR website! X^2-38X-16
THE PROCESS IS TO DEFINE ALL THE FACTORS FOR 5 & -16
1*5=5 ARE THE ONLY FACTORS FOR 5
-1*16, 1*-16, -2*8, 2*-8, -4*4, 4*-4 ARE THE FACTORS FOR -16
NOW YOU NEED TO SELECT THE APPROPRIATE FACTORS SUCH THET THE SUM OF THE PRODUCTS =(-38). THIS IS A TRIAL & ERROR PROCESS BUT THE CLUE IS THE LARGEST FACTOR OF 5 IS 5. SO TO GET THE SUM YOU NEED AT LEAST A NUMBER NEAR 38. THE ONLY FACTOR OF 16 THAT COMES CLOSE IS (8). SO TRY IT.
(5*8)+(1*-2)=40+2=38 BUT THIS IS +38 WE NEED A -38
SO WE TRY
(5*-8)+(1+2)=-40+2=-38
THUS WE HAVE THE FOLLOWING TERMS:
(5X+2)(X-8)
TO PROVE THIS SOLUTION USE THE FOIL TECHNIQUE:
5X*X+5X*-8+2X-16
5X^2-40X+2X-16 NOW COMBINE THE X TERMS WE HAVE
5X^2-38X-16
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