Answer:
STEP
1
:
Equation at the end of step 1
((15 • (y3)) + (2•3y2)) - 21y
STEP
2
:
Equation at the end of step
2
:
((3•5y3) + (2•3y2)) - 21y
STEP
3
:
STEP
4
:
Pulling out like terms
4.1 Pull out like factors :
15y3 + 6y2 - 21y = 3y • (5y2 + 2y - 7)
Trying to factor by splitting the middle term
4.2 Factoring 5y2 + 2y - 7
The first term is, 5y2 its coefficient is 5 .
The middle term is, +2y its coefficient is 2 .
The last term, "the constant", is -7
Step-1 : Multiply the coefficient of the first term by the constant 5 • -7 = -35
Step-2 : Find two factors of -35 whose sum equals the coefficient of the middle term, which is 2 .
-35 + 1 = -34
-7 + 5 = -2
-5 + 7 = 2 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, -5 and 7
5y2 - 5y + 7y - 7
Step-4 : Add up the first 2 terms, pulling out like factors :
5y • (y-1)
Add up the last 2 terms, pulling out common factors :
7 • (y-1)
Step-5 : Add up the four terms of step 4 :
(5y+7) • (y-1)
Which is the desired factorization
Final result :
3y • (y - 1) • (5y + 7)
Step-by-step explanation:
