Question

Find the common factors of the given terms: \[6\]abc, $24$a${{b}^{2}}$, $12{{a}^{2}}$b.

Answer 1

Hint: Polynomials are the combination of variables and arithmetic operations.
All four arithmetic operations – addition, subtraction, multiplication and division can be used to form polynomials.

Complete step by step solution:
Polynomials are the expressions having constants and variables connected to an arithmetic operation that is multiplication.
Polynomials form a strong and essential part of algebra. They are the base from which equations are formed. The equations in turn help in solving problems and undertaking analysis and interpretation. The results derived on the basis of analysis helps in making decisions.
\[6\]abc, $24$a${{b}^{2}}$, $12{{a}^{2}}$b are all types of polynomials.
On the basis of the number of variables, polynomials can be categorized into monomials (one variable), binomials (two variables), trinomial (three variables), polynomials (more than three variables) and etcetera.
On the basis of degree (highest power) of polynomial, polynomials can be categorized as: linear polynomial, quadratic polynomial, cubic polynomial, bi-quadratic polynomial and so on.
Common factors of polynomial are those variables and constant which are common or same in all given polynomials:
In polynomials, \[6\]abc, $24$a${{b}^{2}}$, $12{{a}^{2}}$b, term \[6\]ab is common as first polynomial can be written as \[6\]ab $\times $ c, second polynomial can be written as \[6\]ab $\times \text{ }4$b and third polynomial can be written as \[6\]ab $\times \text{ 2}$a.
This indicates that the common factor of polynomials is \[6\]ab.

Note:
> Common factors of polynomials are the combinations of numbers and variables.
> Common factors are determined and used to find factors of different kinds of polynomials.