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What are the factors of the term 4xyz?

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Algebra is one of the oldest branches of mathematics, dealing with number theory, geometry, and analysis. The study of mathematical symbols and rules includes manipulating these mathematical symbols. Algebra covers practically everything, from solving simple equations to studying abstractions.

Algebra also covers a wide range of subjects, from fundamental problem solving to abstraction studies. Basically concentrated on variables with undefined values. The branch of mathematics deals with variables and arithmetic operations performed across these symbols. These variables have no set values. In our daily lives, we face problems. Certain values are always keep on changing.

These values or variables are frequently represented in algebra by symbols such as a, b, c, d, x, y, z, p, or q. These variables are handled using different mathematical operations such as addition, subtraction, multiplication, and division to determine their values.

Factorization of Polynomials in Algebra

A factor is a number that divides another number without leaving any residual. Simply put, it implies representing a number as the product of two other numbers. Similarly, in Algebra, algebraic formulas are written as a product of their factors.

Factorization is a method for identifying factors for any mathematical object, such as a number, a polynomial, or an algebraic expression. Thus, factorization of an algebraic expression refers to the process of finding out the factors of a given algebraic expression.

For Example: Find out the factors of 5xy2?

Solution:

Given: 

5xy2 , this is a monomial expression

so with the factors of term 5xy2 ,we can write as

= 5 × x × y × y

so the factors of 5xy2 are 5,x,y,y

What are the factors of the term 4xyz?

Solution: 

Given term: 

4xyz

we can factorize the above term

= 4xyz

therefore , 4xyz = 4 × x × y × z

so the factors of 4xyz are 4,x,y,z

Sample Problems

Problem1: Find the factors of expression 4x + 5y?

Solution: 

Given Expression are binomial expression

here , 4x + 5y  , both are unlike terms

factors of term 4x are 4 × x

factors of term 5y are 5 × y

therefore the factors of binomial expression 4x + 5y are 4,x and 5,y

Problem 2: What are the factors of 4a2 + 8?

Solution: 

Given: 

4a2 + 8 

now we will find the common factors and take it as common from the expression :

= 4a2 + 8

here 4 is the common factor 

= 4(a2 + 2)

So the factors are 4 , (a2 + 2) .

Problem 3: What are the factors of the term -15xyz?

Solution: 

Given term:

-15xyz

we can factorize the above term

= -15xyz

therefore , -15xyz

= (-1) ×15 × x  ×  y × z

so the factors of -15xyz are -1,15 ,x,y,z

Problem 4: What are the factors of the term 2xy + 2x2y2

Solution:

Given:

2xy + 2x2y2

To find factors:

= 2xy + 2x2y2

=  (2 × x × y) + (2 × x × x × y × y)

So now we will take out common factors 

=  2xy(1 + xy)

therefore , 2xy , (1+xy ) are the factors of 2xy + 2x2y2 .

Problem 5: What are the factors of xy + x2?

Solution: 

Given:

xy + x2

= x(y + x)

So, the factors of xy + x2 are x and (y+x) .

Problem 6: What are the factors of the term 25xz?

Solution: 

Given term:

25xz

we can factorize the above term

= 25xz

therefore , 25xz

= 25 × x × z

so the factors of 25xyz are 25 , x , z .

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Last Updated : 24 Aug, 2022
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