Factorise by splitting the middle term 12y^2+28y-5
Answers
Step-by-step explanation:
Factoring 12y2+28y-5
The first term is, 12y2 its coefficient is 12 .
The middle term is, +28y its coefficient is 28 .
The last term, "the constant", is -5
Step-1 : Multiply the coefficient of the first term by the constant 12 • -5 = -60
Step-2 : Find two factors of -60 whose sum equals the coefficient of the middle term, which is 28 .
-60 + 1 = -59
-30 + 2 = -28
-20 + 3 = -17
-15 + 4 = -11
-12 + 5 = -7
-10 + 6 = -4
-6 + 10 = 4
-5 + 12 = 7
-4 + 15 = 11
-3 + 20 = 17
-2 + 30 = 28 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -2 and 30
12y2 - 2y + 30y - 5
Step-4 : Add up the first 2 terms, pulling out like factors :
2y • (6y-1)
Add up the last 2 terms, pulling out common factors :
5 • (6y-1)
Step-5 : Add up the four terms of step 4 :
(2y+5) • (6y-1)
Which is the desired factorization
Final result :
(6y - 1) • (2y + 5)
Step-by-step explanation:
Question :12y²+28y-5
Answer :Two number sum=28
product=-60
Number=-2,30
12y²-2y+30y-5
(12y²-2y)+(30y-5)
2y(6y-1)+5(2y+5)
Total Answer:(6y-1) (2y+5)