factor 252s^3g-588s^2g^2+343sg^3

Question

1.factor 252s^3g-588s^2g^2+343sg^3

 

2. by walking 4mph for one period of time and 2mph for another. Roger traveled 18miles.Had he walked 3mph faster throughout, he would have gone 39 miles. How many miles did he work at 4mph.

 

 

Answer 1

1)Notice every term has a s term, a g term, and a factor of 7. Therefore we may write it as 7*s*g(36*S² -84s*g+49*g²). Next notice 36=6², 49=7², and 84=2*6*7. There it may be factored to 7*s*g(6s-7g)².

 

2) Since a boost of 3mph leads to an increase of 21 miles, it implies Roger walked for 7 hours. Now, if he were to walk at 2 mph for the entire trip, he would only travel 14 miles, which is 4 miles too little. Therefore he had to walk for 2 hours at 4 miles to walk 18 miles.