Answer:
5 • (2x + 1) • (x + 1)
Explanation:
Step 1 :
Equation at the end of step 1 :
((2•5x2) + 15x) + 5
Step 2 :
Step 3 :
Pulling out like terms :
3.1 Pull out like factors :
10x2 + 15x + 5 = 5 • (2x2 + 3x + 1)
Trying to factor by splitting the middle term
3.2 Factoring 2x2 + 3x + 1
The first term is, 2x2 its coefficient is 2 .
The middle term is, +3x its coefficient is 3 .
The last term, "the constant", is +1
Step-1 : Multiply the coefficient of the first term by the constant 2 • 1 = 2
Step-2 : Find two factors of 2 whose sum equals the coefficient of the middle term, which is 3 .
-2 + -1 = -3
-1 + -2 = -3
1 + 2 = 3 That's it
Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, 1 and 2
2x2 + 1x + 2x + 1
Step-4 : Add up the first 2 terms, pulling out like factors :
x • (2x+1)
Add up the last 2 terms, pulling out common factors :
1 • (2x+1)
Step-5 : Add up the four terms of step 4 :
(x+1) • (2x+1)
Which is the desired factorization
So the answer is:
5 • (2x + 1) • (x + 1)