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.