Rules in Factoring Numbers

Factoring are the numbers when multiply its get another number. For example 14 the factoring of 2, and 7, 2*7 = 14. some of the factoring numbers have more than one factoring, Here 16 are the number that will be factoring as 4*4, 1*16, 2*8, and 8*2. Here the number that has one time is called prime factoring numbers. These are the rules in factoring numbers.

Rules in factoring numbers with prime:

    The prime factoring numbers deals only the prime factor, Example 8 = 2*2*2. here 8 is the even number that multiplied with 2*2*2, 2 is a prime factorization.

Rules in factoring numbers with quadratic equations:

    There is another way to factoring rules in algebra. Factoring numbers is of quadratic equation. The quadratic equation is in type of ay2+by+c=0. Here y is the variable and other alphabets are constant.

Problems using the rules in factoring numbers:

Problems in factoring numbers:

(i)                  32

Solution: using the rules in factoring numbers,

= 32, will be divided by 2 still to get the remainder 1.

= 2*2*2*2*2.

(ii)                27

Solution: using the rules in factoring numbers,

= 27, will be divided by 7 still to get the remainder 1.

= 3*3*3.

(iii)               64

Solution: using the rules in factoring numbers,

= 64, will be divided by 2 still to get the remainder 1.

= 4*4*4

Problems using  the rules in prime factoring numbers:

(iv)              49

Solution: using the rules in factoring numbers,

= 49, will be divided by 7 still to get the remainder 1.

= 7*7. Here 7 is the prime number

(v)                1331

Solution: using the rules in factoring numbers,

= 1331, will be divided by 11 still to get the remainder 1.

= 11*11*11 here 11 is the prime number.

Problem using the rules in factoring numbers of quadratic equations

Rules in factoring numbers by quadratic equation as 2x2+4x+2 = 0

Solution:  First check the given equation is in the given equation is in the form of quadratic equation a x2+ bx + c = 0. The equation is in the form of  2x2+4x+2 = 0 the equation is satisfied the  quadratic equation.

2x2+4x+2 = 0 taking the coefficient of x square is 1 and the constant term is 2.Here we multiply 2*2 is 4, as the same way we add 2+2 = 4

2x2+4x+2 = 0 here substitute the value in 2x and 2x in the given equation for 4x of the given equation, we get

2x2+4x+2 = 0 the equation satisfies the certain condition

2x2+2x +2x +2 =0 taking the common factor

2x(x+1) + 2(x+1) = 0 in this equation the common factor is (x+1)(x+2).

(2x+2)(x+1) = 0

x=-1 and x = -1 here this is the values for rules in factoring numbers by quadratic equation.

Rules in factoring numbers by quadratic equation as x2+5x+6 = 0

Solution:  First check the given equation is in the given equation is in the form of quadratic equation a x2+ bx + c = 0. The equation is in the form of  x2+5x+6 = 0 the equation is satisfied the  quadratic equation.

x2+5x+6 = 0 taking the coefficient of x square is 1 and the constant term is 2.Here we multiply 2*3 is 6, as the same way we add 2+3 = 5

x2+5x+6 = 0 here substitute the value in 2x and 3x in the given equation for 5x of the given equation, we get

x2+5x+6 = 0 the equation satisfies the certain condition

x2+2x +3x +6 =0 taking the common factor

x(x+2) + 3(x+2) = 0 in this equation the common factor is (x+1)(x+2).

(x+2)(x+3) = 0

x=-2 and x = -3 here this is the values for rules in factoring numbers by quadratic equation.