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**Polynomial**An algebraic expression in which the exponent of variable in each term is a non-negative integer is called a polynomials. A polynomial with variable x is denoted by f(x), g(x), h(x), etc. A polynomial with variable y is denoted by f(y), g(y), h(y) etc.

**Degree of Polynomial**The highest degree of the given polynomial is known as its degree.

E.g. In x + 2, the degree is 1.

In 3x

In x

**Types of Polynomials**

**Monomial**

A polynomial with only one term is called a monomial. E.g. 5x, 6y, 5xy etc.**Binomial**

A polynomial with two terms is called a binomial. E.g. 5x^{2}+ 2x, 2x – 3, 5xy + 4, etc.**Trinomial**

A polynomial with three terms is known as a trinomial. E.g. x^{2}+ 5x + 4, x^{2 }+ 9x + 14, etc.**Multinomial**

A polynomial with more than three terms is called multinomial. E.g. x^{4}+ 2x^{3}+ x^{2 }+ 3x + 2, y^{3}+ 4y^{2}+ 5y + 6 etc.

**Synthetic Division**It is then divided by comparing with division with x-a and a becomes the divisor. Then the quotient is determined with a degree less than the dividend and the last number becomes the remainder.

Example: Divide g(x) = x

Solution:

Comparing with x – a of f(x) then

x – 2 = 0

or x = 0 + 2

\(\therefore\) x = 2

Now,

\(\begin{array}{c|lcr} 2 & 1 & 5 & 6 \\ & & 2 & 14 \\ \hline & 1 & 7 & |20| \\ \end{array}\)

Hence,

Quotient = x + 7

Remainder = 20

**Exercise**

**Find the sum of f(x) = 2x + 3 and g(x) = 9x + 8**

Solution:

Here,

f(x) = 2x + 3

g(x) = 9x + 8

Now,

f(x) = g(x)

\(\begin{matrix} & 2x & + & 3 \\ & 9x & + & 8 \\ \hline (+) & 11x & + & 11 \end{matrix}\)**Find the sum of f(x) = x**Solution:^{3}+ x^{2 }+ 4x + 8 and g(x) = x^{3}+ 3x^{2}– 9x + 20

Here,

f(x) = x^{3}+ x^{2 }+ 4x + 8

g(x) = x^{3}+ 3x^{2}– 9x + 20

Now,

f(x) + g(x) = \( \begin{matrix} & x^3 & + & x^2 & + & 4x & + & 8 \\ (+) & x^3 & + & 3x^2 & - & 9x & + & 20 \\ \hline & 2x^3 & + & 4x^2 & - & 5x & + & 28 \end{matrix}\)

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