snsdfb 3 years ago factor each polynomial completely. 3x^2+ 30x+ 75

1. kumar2006

3x^2+2250x

2. mercedesbenzz

3(x+5)(x+5)

3. Laura*

Hey guys, please explain how you got here to help snsdfb understand the process. Thanks!

4. mercedesbenzz

each term in the trinomial is factorable by 3, so pull out the 3.

5. mercedesbenzz

once you do that youll have 3(x^2+10x+25)

6. mercedesbenzz

so to factor that, find two terms that will multiple to 25, but add to 10, which is 5.

7. mercedesbenzz

so youll have 3(x+5)(x+5). to check your work, simply multiple the parenthesis and then distribute the 3

8. snsdfb

thank you can you explain how to factor 5m^2- 20n^2?

9. mercedesbenzz

both of those terms are divisible by 5. so pull out the 5 from each term. youll have 5(m^2 - 4n^2)

10. mercedesbenzz

since you have more than one variable you cannot factor any further than that.

11. snsdfb

okay got it. how about 2k^3-36k^2+162k?

12. mercedesbenzz

each term is divisible by 2, so divide each term by 2 and youll get 2(k^3-18k^2+81)

13. mercedesbenzz

x is also a common factor, so take out an x from each term

14. mercedesbenzz

so youll have 2k(K^2-18k+81)

15. mercedesbenzz

so now like before find two terms that multiply to positive 81, but add to negative 18, which is -9

16. mercedesbenzz

17. snsdfb

thank you. 12x^3-20x^2+30x-50?

18. mercedesbenzz

pull out a 2x from each term: 2x(6x^2+15x-25)

19. mercedesbenzz

since you have a leading coefficient you can't accurately an answer that has 2 parenthesis. so you will have to plug in each value into the quadratic equation. the quadratic equation is [-b+/-(sqrt((b^2)-(4*a*c)))]/(2*a)

20. snsdfb

i need to factor the polynomial

21. mercedesbenzz

once you plug in all the values your answer will be -15+/--5root33 all over 12

22. mercedesbenzz

that polynomial is not factorable.

23. snsdfb

okay

24. snsdfb

factor the polynomial. 6x^2-2x-20

25. mercedesbenzz

pull out the 2: 2(3x^2-x-10) using the 3 find two numbers that will multiply to -10 but add to -1: (x-2)(3x+5) im not here to do your math homework, if youre having trouble with the process of getting the answer just ask me question about that.