What can you say about the prime factorization of the denominator of 27.142857

about 12 months ago 1 Answer 140 views

What can you say about the prime factorization of the denominator of 27.142857

about 12 months ago 0 Answer 122 views

Ram has two rectangles having their areas as given below:

(1) 25a2-35a+12                   (II) 35y2+13y-12

(i) Given possible expressions for the length and breadth of each rectangle.

(ii) Which mathematical concept is used in this problem?

(iii) Which value is depicted in this problem

 

(i) Possible length and breadth of the rectangle are the factors of its given area.

Area    =  25a^{2}- 35a + 12

          = 25a^{2}-15a - 20 a + 12

          =5a (5a-3) -4 (5a-3)

          = (5a-4) -4 (5a-3)

So possible length and breadth are (5a -3) and (5a - 4) units, respectively.

(ii)  Area  = 35y^{2}+13y-12

              = 35y^{2}+28y-15y-12

              = 7y (5y+4)-3(5y+4)

              = ( 7y - 3) (5y+4)

So, possible length and breadth are (7y-3) and (5y+4) units respectively. 

(ii) Factorization of polynomials 

(iii) Expression of one's desires and news is very necessary.

Check whether 4n can be  end with the digit  0  for any natural number n. 

If the number 4n, for any n, were to end with the digit zero, then it would be divisible by 5.That is, the prime factorization of 4n would contain the prime  5. This is not possible  because 4n = (2)2n ; so the only prime in the factorization of 4n is2. So, the uniqueness of the Fundamental Theorem of arithmetic guarantees that there are no other primes in the factorization of 4n. So there is no natural number  n for which 4n ends with the digit zero  

Divide : 

(i)  9x^{2}y^{2} (3z-24) div 27xy (z-8)

(ii) (y^{2}+7y+10)div (y+5)

(i) For taking 3 common 

frac{9x^{2}y^{2}(3z -24)}{27 xy (z-8)} = frac{xy(3z-24)}{3(z-8)}

frac{ xy(3z-24) }{3z-24}

= xy

For correct answer  = xy 

 

(ii)  For factorization of y^{2}+7y+10

frac{ y^{2}+7y+10}{y+5} = frac{(y+2) (y+5)}{y+5} = y+2

For correct answer  = y+2