Solving Proportions

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Polynomial in math means an equation containing two or more than two term. The word poly means many. Each term can consists of one or more than one unknown variables with different coefficients and constant numbers. Each variable can have different exponent values. The highest exponent is called as the degree of the polynomial. There are various mathematical operations which are used to simplify and solve the given polynomial.

 Example 1: Simplify the polynomial expression, 5 x4 – 2 x3 + x2 – 3 x + 2 when given x = 1.

Solution: The above algebraic expression contains variable ‘x’ with different exponents.

Degree of the polynomial is equal to 4.

So substituting x = 1 in the place of ‘x’ in the above polynomial expression, we get

5 (1)4 –2 (1)3 + (1)2 – 3 (1) + 2

5 (1) –2 (1) + (1) – 3 (1) + 2; 5 - 2+ 1 - 3 + 2 = 3

The value of the above polynomial expression is 3.
 
Example 2: Simplify the polynomial expression, x5 – 5 x3 + x2 + 5 x + 1 when given x = -1.

Solution: The above algebraic expression contains variable ‘x’ with different exponents.

Degree of the polynomial is equal to 5.

So substituting x = -1 in the place of ‘x’ in the above polynomial expression, we get

 (-1)5 –5 (-1)3 + (-1)2 + 5 (-1) + 1

(-1) + 5 (1) + (1) - (5) + 1; -1 + 5 + 1 - 5 + 1 = 1

The value of the above polynomial expression is 1.

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