Factoring Help?

Question

6b^4 -18b^3 -60b^2


Plus a word problem:

If one half a number is subtracted from five sixths of the number, and the difference is 6. WHat is the number ?

Answer 1

6b^4 - 18b^3 - 60b^2

6 is a factor of each coefficient, and b^2 is a factor of each term.
Pull them out to give:

6b^2(b^2 -3b - 10)

Factor the term in parentheses to give:
6b^2(b-5)(b+2)



Now for the word problem:
(5/6)x - (1/2)x = 6

Multiply both sides through by 6:
5x -3x = 36
2x = 36
x = 18

Hope that helps ;)

Answer 2

1. Factor: 6b^4 -18b^3 -60b^2

First: find the greatest common factor which is, 6b^2...

6b^2(b^2 - 3b - 10)

Sec: factor the expression in parenthesis > multiply the 1st & 3rd coefficient to get "-10." Find two numbers that give you "-10" when multiplied & "-3" (2nd/middle coefficient) when added/subtracted. The numbers are (-5 & 2).

*Rewrite the expression with the new middle coefficients...

b^2 - 5b + 2b - 10

*When you have 4 terms --- group "like" terms & factor...

(b^2 - 5b) + (2b - 10)
b(b - 5) + 2(b - 5)
(b - 5)(b + 2)

Third: combine the sets with the greatest common factor...

= 6b^2(b-5)(b+2)

2. Algebraic Equation: (5/6)(x) - (1/2)(x) = 6

First: eliminate fractions --- multiply the denominators with each term...

(6)(2)(5/6)(x)-(6)(2)(1/2)(x)=(6)(2)(6)

Sec: cross cancel "like" terms & combine the remaining terms...

(2)(5)(x)-(6)(1)(x)=(6)(2)(6)
10x - 6x = 72
4x = 72

Third: isolate "x" on one side --- divide both terms by "4"..

4x/4 = 72/4
x = 18

Answer 3

6b^4 -18b³ -60b²
6b²(b² - 3b - 10) = 0
d = -3² - 4.1.-10
d = 9 + 40
d = 49

b = (3 +/- \/49) : 2.1
b' = (3 + 7) : 2
b' = 10 : 2 = 5
b" = (3 - 7) : 2
b" = -4 : 2 = -2
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Solution: {b elements of R| b' = 5 or b" = -2 }
2)
x/2 - 5x/6 - 6 = 0
3x - 5x = 36
-2x = 36
c = 36:-2
x = -18
Solution: {There is x in R| x = -18}

Answer 4

6b^4 - 18b³ 60b²

6b²(b² - 3b - 10)

6b²(b² + 2b - 5b - 10

6b²[b (b + 2) - 5(b + 2)]

6b²(b - 5)(b + 2)

- - - - - - - - - - - - -

5/6x - 1/2x = 6

6(5/6x) = 6(1/2) = 6(6)

5x = 3x = 36

2x = 36

2x/2 = 36/2

x = 18

The number is 18

- - - - - - - - - - - - - -s-

Answer 5

Question 1
=6b²(b² - 3b - 10)
= 6b²(b - 5)(b + 2)

Question 2
(5/6)x - (1/2)x = 6
5x - 3x = 36
2x = 36
x = 18
The number is 18

Answer 6

6b^4 -18b^3 -60b^2 =
6b^2(b^2 -3b -10b^2) =
6b^2(b-5)(b+2)=
6b(b)(b-5)(b-2)

5n/6 -n/2 =6
(5n -3n)/6 = 6
2n =36
n = 18

Answer 7

b^2(6b^2-18b-60)
b^2(2b-10)(3b+6)

Answer 8

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Answer 9

i'm sorry i'm not good in algebra but here is the answer in the word problrm...

let x be the no.
5x/6-1/2=6
5x/6=6+(1/2)
5x/6*(6/5)=13/2*(6/5)
x=39/5

that's the number

hope you'll understand