Question

Classify the polynomial as linear, quadratic, cubic and biquadratic polynomial $ 7{t^4} + 4{t^3} + 3t - 2 $

Answer 1

Hint: Linear polynomial is a type of polynomial as p(x)=ax+b where a and b are real numbers. Whereas a quadratic function is a polynomial of degree 2 such as $ a{x^2} + bx + c $ . Cubic polynomial is a type of polynomial with degree 3 and a biquadratic polynomial is a polynomial of fourth degree.

Complete step-by-step answer:
So, the degree of a polynomial is the highest power of the variable of a polynomial having a non-zero coefficient. So, we will first look at the degree of a polynomial and match it with the corresponding definition of linear, quadratic, cubic and biquadratic polynomials respectively.
So, let’s look one by one. So basically, linear polynomial is a type polynomial of type p(x)=ax+b where a and b are real numbers.
Here we have the equation in the form of $ a{x^4} + b{x^3} + c{x^2} + dx + e $
Here it is not in the form of p(x)=ax+b so the given polynomial is not a linear equation.

Now let’s look into quadratic equations. So basically, a quadratic function is a polynomial of degree 2 as $ a{x^2} + bx + c $ . Here we have the given equation in the form of $ a{x^4} + b{x^3} + c{x^2} + dx + e $
So, this equation is also not satisfying the given equation hence it is not quadratic also.

Let’s look into cubic form so basically cubic form is the type of equation with degree that is $ a{x^3} + b{x^2} + cx + d $
Hence the given equation does not satisfy the cubic equation.

Let’s look into the biquadratic form so we have the given equation in the form of $ a{x^4} + b{x^3} + c{x^2} + dx + e $ which is the same as a biquadratic equation.
Here the given polynomial is in the form of a biquadratic equation.
Hence the given polynomial is in biquadratic polynomial
So, the correct answer is “Biquadratic polynomial”.

Note: In majority of the questions the highest power of the polynomial determines the type of polynomial it is. But sometimes the variable may contain a fractional power and in such case the type of polynomial can’t be determined.