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How do you factor 25b^2-60B+36?

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r4rob92 | Valedictorian

Posted November 3, 2011 at 5:34 AM via web

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How do you factor 25b^2-60B+36?

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mwmovr40 | College Teacher | (Level 1) Associate Educator

Posted November 3, 2011 at 6:00 AM (Answer #1)

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There are a couple of ways of factoring this polynomial.  Brute force and the Quadratic Formula.

By brute force, you need to find factors of 25 and of 36 that will combine to form -60.

Factors of 25                               factors of 36

1, 25                                           1, 36

5, 5                                             2, 18

                                                  3,  12

                                                  4,   9

                                                  6,   6

To get the signs to work our right, we would need for the factors to have subtraction.

Guess 1:

`(5B - 4)(5B - 9) = 25B^2 - 45B - 20B +36 = 25B^2 -65B +36`

Gues 2:

`(5B - 6)(5B -6) = 25B^2 - 30B - 30B + 36 = 25B^2 -60B + 36` as desired.

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mwmovr40 | College Teacher | (Level 1) Associate Educator

Posted November 3, 2011 at 6:07 AM (Answer #2)

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Sorry... I forgot to do the Quadratic Formula method:

assume  `25B^2 -60B + 36 =0`

The Quadratic formula is

`B = (-b +- sqrt(b^2 - 4ac))/(2a)`  where a = 25, b = -60, and c = 36

`B = (60 +- sqrt(3600 - 3600))/(50) = 60/50 = 6/5`  so, putting this into factors:

 `(B - 6/5)(B-6/5) = (B - 6/5)^2 = (5B - 6)^2`

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atyourservice | Student, Grade 10 | Valedictorian

Posted March 22, 2014 at 7:19 PM (Answer #3)

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`25b^2-60B+36  `

find the square root of a and c

they are already perfect squared

`(5b+6)^2 `

`sqrt((5b+6)^2) `

`5b+6`

is the answer but to solve faster set it equal to 0

5b+6=0

`5b=-6`

`b=-6/5`

or 

`-1 1/5`

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