9th grade algebra (factoring)

Can you check the following problems?

Factor the following.
1. x^2 + 9x + 18
= (x + 6)(x + 3)

8. 3x^3 - 24x^2 - 60x
= 3x(x^2 - 8x - 20)
= 3x(x-10)(x + 2)

9. 5x^4 - 5x^3 - 30x^2
= 5x^2(x^2 - x - 6)
= 5x^2(x - 3)(x + 2)

10. 6x^2 - x - 2
= (x - 4/6)(x + 3/6)
= (x -2/3) (x +1/2)
= (3x - 2)(2x + 1)

17. (m^4 - 81)
= (m^2 + 9)(m^2 - 9)
= (m^2 + 9)(m + 3)(m - 3)

18. 4b^2 - 400
= 4(b^2 - 100)
= 4(b + 10)(b - 10)

22. x^2 - 2x - 3 = 0
(x - 3)(x + 1) = 0
x - 3 = 0 x + 1 = 0
x = 3, x = -1

23. 6b^3 - 28b^2 + 30b = 0
2b(3b^2 - 14b + 15) = 0
2b(b - 9)(b - 5) = 0
2b (b-9/3)(b-5/3) = 0
2b(b-3)(3b-5) = 0
2b = 0, b-3 = 0, 3b - 5 = 0
b = 0, b = 3, b = 3/5

24. 5m^2 + 11m - 12 = 0
(m + 15)(m - 4) = 0
(m +15/5)(m -4/5) = 0
(m + 3)(5m - 4) = 0
m + 3 = 0, 5m - 4 = 0
m - -3, m = 4/5

25. 27x^2 - 12 = 0
3(9x^2 - 4) = 0
3(3x - 2)(3x + 2) = 0
3 != 0, 3x - 2 = 0, 3x + 2 = 0
3 != 0, x = 2/3, x = -2/3

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  1. all correct. Good job.

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  2. thanks for checking!!

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