could someone help me with math?

Question

Factor the following trinomial completely. Look first for the greatest common factor.

 

6y²+20y-50

Answer 1

Hi Michael,

 

 

Factor the following trinomial completely. Look first for the greatest common factor.


6y²+20y-50

You have to look for the greatest common factor to all three terms.

1st term 6y²           1*2*3*y*y
2nd term 20y          1*2*2*5*y
3rd term -50          -1*2*5*5

What factor is common to all three? Looks like 2

1st term 6y²              1*2*3*y*y 2 (1*3*y*y) = 2(3y²)
2nd term 20y             1*2*2*5*y 2 (1*2*5*y) =2(10y)
3rd term -50             -1*2*5*5 2 (-1*5*5 ) = 2(-25)

The 2 is factored out and what is left goes in the parentheses.

                                  6y²+20y-50
                                2(3y²+10y-25)
Now factor 3y²+10y-25


I use the Double-Slide method

Take the 1st coefficient and multiply by the last term: y²+10y-3(25)

                                                                         = y²+10y-75
Since the last term is negative, one factor is positive and one negative.
Since the 2nd term is positive, the largest factor is positive.
Factors of -75 which sum 10
-3     25 no
-5     15 yes                (y-5)(y+15)
Since we multiplied by 3 before, now we have to divide by three the get the final factors;
Note: 5/3 cannot be reduced so you slide the 3 before the y to get the entire factor.

                               (y-5/3)(y+15/3)
                                 (3y-5)(y+5)

We must remember to add in the GCF=2 to the final response.


                               2(3y-5)(y+5)

 

The trinomial is fully factored.