Find the complete factored form of the polynomial - 2ab+5a^3b^2

Equation at the end of step 1:

(2a2 - 5a) - 3

Step 2:

Trying to factor by splitting the middle term

2.1 Factoring 2a2-5a-3

The first term is, 2a2 its coefficient is 2.

The middle term is, - 5a its coefficient is - 5.

The last term, "the constant", is - 3

Step-1 : Multiply the coefficient of the first term by the constant 2 • - 3 = - 6

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

-6 + 1 = - 5 That's it

Step-3 : Rewrite the polynomial splitting the middle term using the two factors found in step 2 above, - 6 and 1

2a2 - 6a + 1a - 3

Step-4 : Add up the first 2 terms, pulling out like factors:

2a • (a-3)

Add up the last 2 terms, pulling out common factors:

1 • (a-3)

Step-5 : Add up the four terms of step 4:

(2a+1) • (a-3)

Which is the desired factorization

Final result:

(a - 3) • (2a + 1)