6y^2-13y-5
(3x+1)(2x-5)
12
To simplify the expression 6y^2 - 13y - 5, we can use a technique called factoring. The goal is to write the expression as a product of two binomials. Here's how you can do it:
Step 1: Look for common factors, if any. In this case, there are no common factors among all three terms.
Step 2: Identify two numbers whose product equals the product of the leading coefficient (6) and the constant term (-5), and whose sum equals the coefficient of the middle term (-13). In this case, the product of 6 and -5 is -30, and we need to find two numbers that multiply to -30 and add up to -13. Those numbers are -15 and 2.
Step 3: We will now split the middle term of the expression using the two numbers we found in Step 2. Rewrite the expression as follows:
6y^2 - 15y + 2y - 5
Step 4: Group the terms in pairs, and factor out the greatest common factor from each pair:
(6y^2 - 15y) + (2y - 5)
3y(2y - 5) + 1(2y - 5)
Now, notice that we have a common binomial factor, (2y - 5), in both terms. We can factor this out:
(2y - 5)(3y + 1)
So, the simplified expression is (2y - 5)(3y + 1).