Question

What is the degree of the polynomial in this expression \[2{x^7} + 4 - 3{x^3} + 5{x^8} - 4x\] ?

Answer 1

Hint: We have to find the degree of the polynomial in this expression \[2{x^7} + 4 - 3{x^3} + 5{x^8} - 4x\]. We will write the given expression in decreasing power of \[x\] then we will ignore the coefficients and write only variables with their powers. At last, we will check which is the highest power of the variable and that is the degree of the polynomial.

Complete step by step answer:
The highest power of the variable in the polynomial is called the degree of the polynomial.We have to find the degree of the polynomial in this expression \[2{x^7} + 4 - 3{x^3} + 5{x^8} - 4x\]. For this, we have to first combine the like terms if any. But in this question, there are not any like terms.

Now, we will write the given expression in decreasing power of \[x\]. So, we get the given expression as \[5{x^8} + 2{x^7} - 3{x^3} - 4x + 4\]. Now, we will ignore the coefficients and write only variables with their powers. So, we get the given expression as \[{x^8} + {x^7} - {x^3} - x\]. Now we will check which is the highest power of the variable and that is the degree of the polynomial. Here, we can see that the highest power of the variable is \[8\].

Therefore, the degree of the polynomial in this expression \[2{x^7} + 4 - 3{x^3} + 5{x^8} - 4x\] is \[8\].

Note: If all the coefficients of a polynomial are zero, we get a zero polynomial. The degree of a zero polynomial is undefined because \[f(x) = 0\], \[g(x) = 0x\], \[h(x) = 0{x^2}\], etc. all are the zero polynomial. Any non-zero number is said to be zero-degree polynomial if \[f(x) = a\] as we can write it in the form \[f(x) = a{x^0}\], where \[a \ne 0\].