For example: \(3x^2 + 4x - 1\)
There are \(3\) terms:
First term: \(3x^2\)
Second term: \(4x\)
Third term: \(- 1\)
For example:
1) \(5xy^2\) and \(5x^2y\) are unlike terms as they do not have same literal factors because the power of \(x\) and \(y\) are not same in the terms.
2) \(5x\) and \(5y\) are unlike terms as they do not have same literal factors because in \(5x\), the literal factor is \(x\) whereas in \(5y\), it is \(y\).
A \(- 7yz\)
B \(6zy\)
C \(- 5 y^2z\)
D \(10yz\)
A term of an expression having no literal factor is called constant term.
For example: \(x^2 + y^2+ 2\)
Here, \(2\) is the term which does not have a literal factor.
Thus, the constant term is \(2\).
A \(x^3\)
B \(3\)
C \(x^2\)
D \(Both\,x^3 and \,x^2\)
Factors
For example: \(5x\)
Here, \(5\) and \(x\) are factors of \(5x\).
Numerical factor
For example: \(5xy^2\)
Here, \(5\) is a numerical factor of \(5xy^2\).
Note: A numerical factor can be a whole number, an integer, a fraction or a decimal.
For example:
1) \(3xyz\) and \(-6xyz\) are like terms as they have same literal factors \((xyz)\) having the same power.
2) \(6x^2y^3\) and \(-16 x^2 y^3\) are like terms as they have same literal factors \(x^2y^3\) having the same power.
For example: (i) \(3xyz\)
Here, \(3yz\) is the coefficient of \(x\).
\(3xy\) is the coefficient of \(z\).
\(3xz\) is the coefficient of \(y\).
(ii) \(5 (x+3)\)
Here, \(x+3\) is the coefficient of \(5\).
\(5\) is the coefficient of \(x+ 3\).
For example: \(3xyz^2\)
Here, \(x\), \(y\) and \(z^2\) are literal factors of the given expression.