The greatest common factor (GCF) of 15ab and 5b2 is 5b.
The GCF is 5b.
4a2 - 20ab2 + 25b4 (2a - 5b2)(2a - 5b2) (2a - 5b2)2
b3 - 5b2 + 12 = (b - 2)(b2 - 3b - 6)Check:(b - 2)(b2 - 3b - 6)= b(b2 - 3b - 6) - 2(b2 - 3b - 6)= b3 - 3b2 - 6b - 2b2 + 6b + 12= b3 - 5b2 + 12
It is: (-5b+2)(b-1) with the help of the quadratic equation formula
5a2 - 20ab - 25b2 = 5(a2 - 4ab - 5b2) = 5(a2 - 4ba - 5b2) since -5b*b = -5b2 and -5b + b = -4b, then = 5(a - 5b)(a + b)
12ab + 13b + 4 (assuming there's addition in the spaces)
5b2 = 8b therefore 5b =8 therefore b = 1.6
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Suppose we start with the opposite view. That is, the square root of 5 is rational. This means that it can be expressed as a ratio of two integers. Let the square root of 5 in its simplest terms be a/b so that a and b are integers with no common factors and b > 0.sqrt(5) = a/b so 5 = a2/b2that is, 5b2= a25 is a factor of the left hand side (LHS) so 5 must be a factor of the right hand side (RHS).Since 5 is a prime and a is an integer, 5 must be a factor of a. That is, a = 5c for some integer c and since a and b are coprime b and c must also be coprime.But now,5 = (5c)2/b2so that 5 = 25c2/b2and so b2= 5c2. As before, this implies that 5 must be a factor of b. But that contradicts the supposition that a and b are coprime.The contradiction implies that the original assumption was incorrect. That is, sqrt(5) cannot be rational.
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