Question

algebra 2 5.2 decide whether the function is a polynomial function. if it is, write the function in standard form and state the degree,

Answer 1

Yes, the specified function  $f(x) = \frac{1}{7} x - 4x^2 +4x^4 - 1$ is a Polynomial Functions.

Polynomial Functions:

Polynomial functions are functions that take only non-negative integer powers or positive integer exponents of variables in equations such as quadratic, cubic, etc. For example, 2x+5 is a polynomial with exponent equal to 1.

There are different kinds of polynomial functions based on the degree of the polynomial. The most common types are:

1. Constant polynomial function: P(x) = a = ax0
2. Zero polynomial function: P(x) = 0; where ai are all zeros, i = 0, 1,…, n.
3. Linear Polynomial function: P(x) = ax + b
4. Quadratic polynomial function: P(x) = ax2+bx+c
5. Cubic polynomial function: ax3+bx2+cx+d
6. Quarter polynomial function: ax4+bx3 +cx2 +dx +e

According to the Question:

The standard form is

$f(x) = 4x^4 -4x^2 + \frac{1}{7} x - 1$

The polynomial degree is 4.

Main coefficient is 4.

The given polynomial is

      $f(x) = \frac{1}{7} x - 4x^2 +4x^4 - 1$

Therefore, The standard form is

$f(x) = 4x^4 -4x^2 + \frac{1}{7} x - 1$

The greatest power of the variable is known as the degree.

So the coefficient of the variable with the highest power of degree 4

is called the leading coefficient.

So the leading coefficient is 4.

Learn more about Polynomial Function:

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