The Exercise Correction 4 natural integers numbers

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1) 
a= x²-5x+4=x²- 2 x +1- 3 x +3 =(x - 1 )² - 3 (x- 1)
=(x - 1 )(x - 1 - 3 )=(x - 1 )(x - 4 )

b =2x²+3x-2 =2x²+4x- x -2 =2x  (x +2 )-(x +2 )
=(x +2 )(2 x - 1 ) 

2) 

3) 

4) the product of two consecutive integers is a natural even number

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Solved Exercise 4 natural integers numbers

Correction

1) factorize the following expression:

a= x²-5x+4

 b= 2x²+3x-1

2) decompose 3240 and 1440 into a product of primes numbers

3) conclude a simple expression for the two numbers(the square root of 3240 and 1440)

4) k is a natural number, show that k (k +1) is an even number

Correction

The Exercise Correction 3 natural integers numbers

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1) we have for all primes numbers greater than 3 is are odd number , so there is an integer k for p = 2k +1

then :

2) we have and p is a prime number  greater than 3 ,so there are tow integers numbers a and b deux nombres entiers naturels such as and  : While a and b are consecutive

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Solved Exercise 3 natural integers numbers

Correction

1) p is a prime number greater than 3

Set out : :

         a) verify that a and b are integers natural

         b) calculate: as a function of p

2) show that every prime number p greater than 3 , is written as a subtraction of two consecutive integers natural

Give this subtraction for P=41

Correction

The Exercise Correction 2 natural integers numbers

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1) 49 is not a prime number because may be divided by 7
we have the following numbers  2  ،  3  ،  5  ،  7  ،  11   ،  13  et 17 do not divide 239 and we have 17²>239>23²
then 239 is a prime number
.......................................................
2) the decomposition into prime numbers : 

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Solved Exercise 2 Natural number

correction

1) identify the primes numbers of the following numbers :49  ،  239   ،   407  ،   387  ،   1559  ،    8367 

2) decompose the following numbers into prime numbers:   675  ،  1650  ،      5292    ،    6250 

  

correction

The Exercise Correction 1 natural integers numbers

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1) showing that a is a multiple of 3:

we have:

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