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

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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.

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`

`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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