Question

write the following polynomial in standard form

3x - 2 + 5x^4 - 4x^3 + x^2

what is the degree of the polynomial?

What is the leading coefficient of the polynomial

Answer 1

The degree of the polynomial is 4 because that is the largest exponent in the expression and 5 is the leading coefficient

Answer 2

$\text{Consider the polynomial}\\ \\ 2x-2+5x^4-4x^3+x^2\\ \\ \text{to write it in standard form, we arrange the terms in decreasing}\\ \text{order of the exponent of the variable x.}\\ \text{so in standard form, the polynomial is}\\ \\ 5x^4-4x^3+x^2+2x-2\\ \\ \text{We can see that the higest exponent that appears on the variable x is 4,}\\ \text{so the degree of the polynomial is 4.}$

$\text{After arranging on the standard form, we can see that the coefficient of}\\ \text{the highest exponent term is 5.}\\ \text{so the leading coefficient is 5.}$

Hence the degree of the polynomial is 4 and the leading coefficient of the polynomial is 5