I need help soving this problem.

Factor the trinomial completely.

4x^3-10x^2-50x

I also want to know if I soved this problem correctly?

Factor the trinomial 9s^2+3s-20

my answer is
(3s-4)(3s+5)

(3s-4)(3s+5) is correct.

For the other, factor out the 2x first, leaving
2x(2x^2 - 5x - 25)
2x(2x+5)(x-5)

after one month of operation the health information services at community health center determined that there were two records misfiled out of the 450 active records. what is the filing accuracy rate for this area?

Information: Juan plans to build a bookcase t store his paperback books, DVDs, and CDs. he has lumber that he will use for the sides and back of the bookcase. Juan plans for his bookcase to have five shelves including, the top and bottom shelves. Each shelf will be 2 1/2 feet long.

Question: Juan bought a piece of pine limber that is 18 feet long. Does he have enough lumber to make the five shelves? If not, how much more does he need? If so, how much will be left over?
Juan measured the location of his bookcase and realized that he could only fit a bookcase with shelves that are 1 3/4 feet wide. What is the maximum number of shelves Juan could build for this new bookcase using the lumber he bought?

Sure! I can help you solve the problem and check if your answer is correct.

To factor the trinomial 4x^3 - 10x^2 - 50x, we first look for the greatest common factor (GCF) among the terms. In this case, the GCF is 2x, so we can factor it out:

2x(2x^2 - 5x - 25)

Now, we need to factor the quadratic trinomial 2x^2 - 5x - 25 further. We can do this by factoring it into two binomials:

2x(2x^2 - 10x + 5x - 25)

Next, we can factor by grouping:

2x(2x(x - 5) + 5(x - 5))

Now, we can see that we have a common binomial factor, (x - 5). We can factor it out:

2x(x - 5)(2x + 5)

So, the fully factored form of 4x^3 - 10x^2 - 50x is 2x(x - 5)(2x + 5).

Now, let's check your answer for the trinomial 9s^2 + 3s - 20. You said your answer is (3s - 4)(3s + 5).

To check if this answer is correct, we can use the distributive property to multiply the factors:

(3s - 4)(3s + 5) = 3s × 3s + 3s × 5 - 4 × 3s - 4 × 5
= 9s^2 + 15s - 12s - 20
= 9s^2 + 3s - 20

As we can see, your answer, (3s - 4)(3s + 5), matches the original trinomial, 9s^2 + 3s - 20. Therefore, your answer is correct!

I hope this helps! Let me know if you have any further questions.