-3p 3 + 5p + (-2p 2) + (-4) - 12p + 5 - (-8p 3) simplyfied

Step by step solution :Step 1 :Skip Ad
Equation at the end of step 1 : ((8•(p3))+(16•(p2))) (2p-10) ———————————————————— ÷ —————————————— (20p+40) ((2p2-12p)+10) Step 2 : 2p - 10 Simplify —————————————— 2p2 - 12p + 10 Step 3 :Pulling out like terms :

3.1 Pull out like factors :

2p - 10 = 2 • (p - 5)

Step 4 :Pulling out like terms :

4.1 Pull out like factors :

2p2 - 12p + 10 = 2 • (p2 - 6p + 5)

Trying to factor by splitting the middle term

4.2     Factoring  p2 - 6p + 5

The first term is,  p2  its coefficient is  1 .
The middle term is,  -6p  its coefficient is  -6 .
The last term, "the constant", is  +5

Step-1 : Multiply the coefficient of the first term by the constant   1 • 5 = 5

Step-2 : Find two factors of  5  whose sum equals the coefficient of the middle term, which is   -6 .

-5 + -1 = -6 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above,  -5  and  -1
                     p2 - 5p - 1p - 5

Step-4 : Add up the first 2 terms, pulling out like factors :
                    p • (p-5)
              Add up the last 2 terms, pulling out common factors :
                     1 • (p-5)
Step-5 : Add up the four terms of step 4 :
                    (p-1)  •  (p-5)
             Which is the desired factorization

Canceling Out :

4.3 Cancel out (p-5) which appears on both sides of the fraction line.

Equation at the end of step 4 : ((8•(p3))+(16•(p2))) 1 ———————————————————— ÷ ——— (20p+40) p-1 Step 5 :Equation at the end of step 5 : ((8•(p3))+24p2) 1 ——————————————— ÷ ——— (20p+40) p-1 Step 6 :Equation at the end of step 6 : (23p3 + 24p2) 1 ————————————— ÷ ————— (20p + 40) p - 1 Step 7 : 8p3 + 16p2 Simplify —————————— 20p + 40 Step 8 :Pulling out like terms :

8.1 Pull out like factors :

8p3 + 16p2 = 8p2 • (p + 2)

Step 9 :Pulling out like terms :

9.1 Pull out like factors :

20p + 40 = 20 • (p + 2)

Canceling Out :

9.2 Cancel out (p + 2) which appears on both sides of the fraction line.

Equation at the end of step 9 : 2p2 1 ——— ÷ ————— 5 p - 1 Step 10 : 2p2 1 Divide ——— by ————— 5 (p-1)

10.1 Dividing fractions

To divide fractions, write the divison as multiplication by the reciprocal of the divisor :

2p2 1 2p2 p - 1 ——— ÷ ——————— = ——— • ————— 5 (p - 1) 5 1
Final result : 2p2 • (p - 1) ————————————— 5