How does writing a polynomial in standard form help you name the polynomial?
We usually put them in order of highest to lowest in terms of exponents.
That way by just looking at the first term exponent we can tell what degree the polynomial has
e.g. 7x^5 - 4x^2 + 3x +9 is a fifth degree polynomial
Trinity is your last name Cha?
Writing a polynomial in standard form helps you name the polynomial by allowing you to easily identify its degree and its leading coefficient.
To write a polynomial in standard form, you arrange the terms in descending order of their degrees. The degree of a term refers to the exponent on the variable. For example, in the polynomial 3x^2 + 2x - 1, the term with the highest degree is 3x^2, and it is written first. The terms with lower degrees, 2x and -1, are written in decreasing order after that.
On the other hand, the leading coefficient is the coefficient of the term with the highest degree. In the polynomial 3x^2 + 2x - 1, the leading coefficient is 3.
Naming a polynomial is often determined by its degree. The degree is the highest power of the variable in the polynomial. For instance, if the polynomial has a degree of 2, it is called a quadratic polynomial. If the degree is 3, it is called a cubic polynomial. If the degree is 4, it is called a quartic polynomial, and so on.
Additionally, the sign of the leading coefficient also plays a role in naming the polynomial. For example, if the leading coefficient is positive, the polynomial is classified as a "positive" polynomial. If the leading coefficient is negative, it is classified as a "negative" polynomial.
By writing a polynomial in standard form, you can easily determine its degree and leading coefficient, which are crucial in naming the polynomial accurately.