Question

Hello, I need help with factoring this equation. It's supposed to have three parentheses but I am only familiar with two (and still having trouble with that).
Enter the dimensions of a rectangular box with a volume of 50b3 - 3 - 2b + 75b2.

Answer 1

cubics have a formula similar to quadratics ...

Answer 2

IF we try a more brute method ... just expanding a general cubic setup and comparing, it may be simple or not so simple to compare parts

Answer 3

(x + a)(x + b)(x + c)

(x^2 + 2ab x + ab)(x + c)

x^3 + 2ab x^2 + ab x
c x^2 + 2abc x + abc
------------------------------
x^3 +(2ab+c)x^2 + (ab+2abc)x + abc

Answer 4

50b3 - 3 - 2b + 75b2

50b^3+ 75b^2 - 2b - 3

50 x^3+ 75 x^2 - 2 x - 3

x^3+ 75/50 x^2 - 2/50 x - 3/50
x^3 +(2ab+c)x^2 + (ab+2abc)x + abc

Answer 5

or if we make them decimals ... *2/2

x^3+ 1.50 x^2 - .04 x - .06
x^3 +(2ab+c)x^2 + (ab+2abc)x + abc

2ab + c = 1.50
ab+2abc = .04
abc = -.06

3 equations in 3 unknowns to play with

Answer 6

2ab + c = 1.50
ab+2abc = .04
abc = -.06 <--

ab+2(.06) = .04

ab = .04 - 2(.06)

c = 1.50 - 2ab

c = 1.50 - 2(.04 - 2(.06))

seens to wirk itself out

Answer 7

*seems to work itself out lol

Answer 8

and i dropped a negative but thats easily remedied ... should be -.06

Answer 9

Very good

But how do we find a and b?

Answer 10

since we know c, we replace it in the original setup and work it out for a and b, which im assuming plays nice since i havent tried it

Answer 11

50b^3 + 75b^2 - 2b-3 Factor by grouping.
= 25 b^2 (2b+3) - 1 (2b + 3)
= (25 b^2 - 1) (2b+3)
Now you can factor the first part because it's a difference of squares.
= (5b - 1)(5b + 1)(2b+3)

Answer 12

c = 1.18 ...

2ab + 1.18 = 1.50
ab+2ab(1.18) = .04
ab(1.18) = -.06


2ab = 1.50 - 1.18

ab = (1.50 - 1.18)/2

etc ...

Answer 13

grouping seems to be nice .... i never was good at grouping for some reason lol

Answer 14

my idea has a tendency to introduce errors since theres more work involved. jam333 did very good

Answer 15

So if the volume = (5b-1)(5b+1)(2b+3) and you need to give dimensions for a possible rectangular box, let's try b=1. That leads to the sides being 4, 6 and 5. There will be many possible answers. When b=2, the box would have sides 9, 11 and 7.

Answer 16

(x + a)(x + b)(x + c)

(x^2 + 2ab x + ab)(x + c)
^^^^
one error i see in mine ... (a+b) x, its a perfect square that has a=b ugh

Answer 17

Thank you everyone for your replies, I'm sorry I should've mentioned I was trying to factor by grouping :)

Answer 18

yes, that would have been some nice information to have lol