Key Features of Polynomials

All terms are written in descending order according to the exponents.

All terms are written in ascending order according to the exponents.

The highest exponent is always zero.

The coefficients are always positive.

h(x) = x⁴ - (1/4)x² + 3

g(x) = 7x - √3 + πx²

f(x) = 5x² + 3x^-1 - x

k(x) = x + 2^x - 0.6x⁵

For even degree and positive leading coefficient, both ends go up.

For odd degree and positive leading coefficient, both ends go down.

For even degree and negative leading coefficient, both ends go up.

For odd degree and negative leading coefficient, both ends go up.

$$f\left(x\right)\rightarrow\infty\ as\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\ as\ x\rightarrow-\infty$$

$$f\left(x\right)\rightarrow\infty\ as\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty\ as\ x\rightarrow-\infty$$

$$f\left(x\right)\rightarrow-\infty\ as\ x\rightarrow\infty,\ f\left(x\right)\rightarrow\infty\ as\ x\rightarrow-\infty$$

$$f\left(x\right)\rightarrow-\infty\ as\ x\rightarrow\infty,\ f\left(x\right)\rightarrow-\infty\ as\ x\rightarrow-\infty$$

The degree is the highest exponent, while the leading coefficient is the number in front of the variable with the highest exponent.

The degree is the number in front of the variable, while the leading coefficient is the highest exponent.

The degree is always 1, while the leading coefficient is always 0.

The degree and leading coefficient are always the same.