im having an brain freeze....i cant remember how to factor..f(x)=2x^2-7x-30..please explain so i can do it on my own

(2X+5)(X-6)

okay if u want to put it in an diamond problem....how do u do that

Sure! I'll be happy to explain how to factor the quadratic function f(x) = 2x^2 - 7x - 30.

To factor a quadratic trinomial like this, you're looking for two binomials that, when multiplied together, equal the original trinomial. In this case, the binomials will take the form (ax + b)(cx + d).

Here's a step-by-step process to factor the quadratic equation:

Step 1: Multiply the coefficient of the x^2 term (2 in this case) by the constant term (-30 in this case). The product is -60.

Step 2: Identify two numbers whose product is -60 and whose sum is the coefficient of the x term (-7 in this case). In this case, the numbers are -10 and 6.

Step 3: Rewrite the middle term (-7x) using the two numbers found in Step 2. Replace -7x with -10x + 6x.

Step 4: Group the four terms into two pairs:
2x^2 - 10x + 6x - 30

Step 5: Factor by grouping. Factor out a common factor from the first two terms and then factor out a common factor from the last two terms:
2x(x - 5) + 6(x - 5)

Step 6: Notice that (x - 5) is a common factor for both terms. Factor it out:
(x - 5)(2x + 6)

And there you have it -- f(x) = (x - 5)(2x + 6) is the factored form of the quadratic function.

Remember, practice makes perfect! Try factoring other quadratic functions to get more comfortable with the process.