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Classify the following as linear, quadratic and cubic polynomial:
\[y+{{y}^{2}}+4\]

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Last updated date: 21st Jul 2024
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Answer
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Hint: Such questions are quite simple to understand and easy to implement. To solve it effectively and efficiently we need to understand some of the basic topics of mathematics like polynomials, quadratic and linear equations and graphs. Before starting to solve the problem, we need to first understand what polynomials, linear, quadratic and cubic equations are. We define polynomials as any equation that contains some variables or unknown parameters as well as some constant terms, which in general represent some kind of a geometry on the coordinate plane when plotted. Polynomials which are of one variable and are equated to zero are used to find the value of the unknown parameter.

Complete step by step answer:
Now we start off with the solution to the given problem by defining the terms linear, quadratic and cubic equations. Any equation in which the maximum power of an unknown parameter or a variable is one, is known as a linear equation. Similarly, an equation in which the maximum power is two, is known as a quadratic equation or a quadratic polynomial and in which the maximum power is three is called a cubic polynomial or cubic equation.
In the given problem, the equation \[y+{{y}^{2}}+4\] has ‘y’ as the unknown parameter or a variable and we can see that the power of ‘y’ in this equation is one and two out of which two is the maximum power. Hence we can clearly say that the given equation is a quadratic polynomial.

Note: Solving such problems might be difficult if we are not aware of chapters like polynomials, quadratic, linear and cubic equations. We need to be very careful while we judge for the maximum power of a variable or an unknown parameter. We also must remember that the number of variables or the unknown parameters do not affect the maximum power of the given equation.