Sample Problems

Problem 1: 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, 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 common factors and take it as common from the expression:

= 4a² + 8

Here 4 is the common factor 

= 4(a² + 2)

So, 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, 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, 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 factors of 25xyz are 25, x, z.

Factors of an algebraic term are the expressions or variables that, when multiplied together, produce the given term. Factors of term 4xyz are, 4, x, y, and z. The solution for the same is added below.