Answer:
20(x+15)(x+10)
Step-by-step explanation:
Hi there!
As your question states, we need to fully factor the polynomial: 20x²+500x+3000
These are pretty big numbers; let's pull out the GCF, as that will make it easier to factor
the GCF is 20
so factoring 20 out of the polynomial will get:
20(x²+25x+150)
As you can see, the polynomial inside the parenthesis is a lot easier to factor than the original with really big numbers.
Now use FOIL to factor x²+25x+150 into 2 binomials
25 is the sum of the last terms
150 is the product of the last terms
think: which two numbers add up to 25 but multiply to get 150?
those two numbers are 15 and 10
x²+25x+150 factored is (x+15)(x+10)
but remember we have the 20 in front of x²+25x+150 (or now, (x+15)(x+10))
therefore the fully factored binomial is 20(x+15)(x+10)
Hope this helps! :)
