Famous Irrational Numbers Famous Irrational Numbers Factoring of a number means finding out the numbers that divide the given number and their multiplication is equal to the given number. Factorization is the method of finding the factors just like the factors of 12 are ( 1 * 2 * 2 * 3 ) For example: ( a2 + 4. a + 3 ) = ( a + 3 ) ( a + 1 ) ,these two are factors of the given expression and for cross checking the answer when we again multiply these factors we find the same expression ( a2 + 4 a + 3 ) as our answer . In simple words we explain the term factorization as the process of finding the expression when the factors will be multiplied . In this process we break the expression in the parts and these parts of expression are known as the factors of the algebraic expression .Here we will talk about Factoring Algebra.
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Example no ( 1 ) : 2 s + 6 is an algebraic expression then factors of this are found as-: 2s is shown as 2s=2*s and 6 = 2 * 3 ( both the terms have 2 as common factor ) then 2 s + 6 is define in form of factors as 2 s + 6 = 2 ( s + 3 ) . Here the factors of this expression are 2 and ( s + 3 ) . Example no ( 2 ) : There is an expression as 3 t2 + 12 t ( it should be noted that the factors are highest common factor ) then we find the factors of given expression . 3 t2 + 12 t have 3 and 12 as a constant values and they have the common factor 3 .So the given expression is also written as 3 t2 + 12 t = 3 ( t2 + 4 t ) is also a factor of this given expression but it would be better as if we write the above given expression as 3 t2 + 12 t = 3 t ( t + 4 ) because 3 t2 is written as 3t * t and 12. t is written as 3 t * 4 then in both the expressions 3t is common and it is written as 3 t ( t + 4 ) that is the factorization of the expression . It is cross checked as if we multiply the terms as 3 t * t + 3 t * 4 then it provides same expression as given i.e. 3 t2 + 12 t . Factorization is the process of changing the sum of products into the products of sum. We use distributive property for Factoring Algebra. Some examples are :
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If there is an expression as 4 p3 q4 r3 + 2 p2 q3 r4 then the factors of the expression are found as 4 p3 q4 r3 = 4 * p * p * p * q * q * q * q * r * r * r 2 p2 q3 r4 = 2 * p * P * q * q * q * r * R * r * r * r then the common factor is 2 p2 q3 r3 and the expression is written as 4 p3 q4 r3 + 2 p2 q3 r4 = 2 p2 q3 r3 ( 2 p q+ r ).
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