Final answer:
To factor the expression 2h² - 5h - 3, use factoring by grouping.
The factored form is (2h + 1)(h - 3).
Step-by-step explanation:
In this case, let's use factoring by grouping.
First, we multiply the coefficient of the quadratic term (2) by the constant term (-3).
This gives us -6.
Next, we need to find two numbers that multiply to -6 and add up to the coefficient of the linear term (-5) in the middle.
The numbers are -6 and 1.
So, we rewrite the expression as:
2h² - 6h + h - 3
Now, we can factor out the greatest common factor from the first two terms and the last two terms:
2h(h - 3) + 1(h - 3)
We have a common binomial factor of (h - 3).
So, the factored form of the expression is:
(2h + 1)(h - 3).