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Question

Which of the following expressions are polynomials in one variable and which are not?

State reasons for your answer. (i) y2+2 (ii) 3t+t2 and (iii) x10+y3+t50.


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Solution

Step 1: (i): Determine whether the expression y2+2 is a polynomial in one variable or not.

A polynomial is defined as a mathematical equation with one or more terms made up of variables, constants, and exponents that are mixed using operations like addition, subtraction, multiplication, and division.

The expression y2+2 can be written as follows:

y2+2=y2+2y0

In the given expression, y is the variable that has powers 2and0, which are whole numbers.

Hence, y2+2 is a polynomial in one variable.

Step 2: (ii) Determine whether the expression 3t+t2 is a polynomial in one variable or not.

The expression 3t+t2 can be written as follows:

3t+t2=3t12+t2

In the given expression, t is the variable that has power 12, which is not a whole number.

Hence, 3t+t2 is not a polynomial in one variable.

Step 3: (iii): Determine whether the expression x10+y3+t50 is a polynomial in one variable or not.

In the given expression, x,y,t are the variables that have powers 10,3,and50, which are whole numbers.

Hence, x10+y3+t50 is not a polynomial in one variable.


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