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Identify constant, linear, quadratic and cubic polynomials from the following polynomials:$ p(x)=2 x^{2}-x+4 $
Given:
\( p(x)=2 x^{2}-x+4 \)
To do:
We have to classify the given polynomial as constant, linear, quadratic and cubic polynomial.
Solution:
Polynomials are expressions in which each term is a constant multiplied by a variable raised to a whole number power.
A constant polynomial is a polynomial of degree 0.
A linear polynomial is a polynomial of degree 1.
A quadratic polynomial is a polynomial of degree 2.
A cubic polynomial is a polynomial of degree 3.
A biquadratic polynomial is a polynomial of degree 4.
A polynomial's degree is the highest or the greatest power of a variable in a polynomial equation.
To find the degree, identify the exponents on the variables in each term, and add them together to find the degree of each term.
In \( p(x)=2 x^{2}-x+4 \), the term $2x^2$ has a variable of power $2$.
This implies the degree of \( p(x)=2 x^{2}-x+4 \) is $2$.
Therefore, the given polynomial is a quadratic polynomial.
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