Determine which functions are polynomial functions. For those that are, identify the degree. $f\left(x\right)=5x^2+6x^3$

Determine which functions are polynomial functions. For those that are, identify the degree. $g\left(x\right)=7x^5-\pi x^3+\frac{1}{5}x$

Determine which functions are polynomial functions. For those that are, identify the degree. $h\left(x\right)=7x^3+2x^2+\frac{1}{x}$

Determine which functions are polynomial functions. For those that are, identify the degree. $f\left(x\right)=x^{\frac{1}{2}}-3x^2+5$

Determine which functions are polynomial functions. For those that are, identify the degree. $f\left(x\right)=(x^2+7)/x^3$

Determine which functions are polynomial functions. For those that are, identify the degree. $f\left(x\right)=(x^2+7)/3$

Identify which graphs are not those of polynomial functions.

Identify which graphs are not those of polynomial functions.

In Exercises 15–18, use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).] <IMAGE>

$f\left(x\right)=-x^4+x^2$

In Exercises 15–18, use the Leading Coefficient Test to determine the end behavior of the graph of the given polynomial function. Then use this end behavior to match the polynomial function with its graph. [The graphs are labeled (a) through (d).] <IMAGE>

$f\left(x\right)=(x-3{)}^2$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=5x^3+7x^2-x+9$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=11x^3-6x^2+x+3$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=5x^4+7x^2-x+9$

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. f(x)=11x⁴−6x²+x+3

Use the Leading Coefficient Test to determine the end behavior of the graph of the polynomial function. $f\left(x\right)=-5x^4+7x^2-x+9$

Find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x)=2(x−5)(x+4)²

Find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x)=3(x+5)(x+2)²

Find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. f(x)=−3(x+1/2)(x−4)³

Find the zeros for each polynomial function and give the multiplicity for each zero. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each zero. $f\left(x\right)=x^3+7x^2-4x-28$

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x³−x−1; between 1 and 2

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x³−4x²+2; between 0 and 1

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers.f(x)=2x⁴−4x²+1; between -1 and 0

In Exercises 33–40, use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x⁴+6x³−18x²; between 2 and 3

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=x³+x²−2x+1; between -3 and -2

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=3x³−10x+9; between -3 and -2

Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x)=3x³−8x²+x+2; between 2 and 3

Divide using long division. State the quotient, and the remainder, $r\left(x\right)$. $(6x^3+7x^2+12x-5)÷(3x-1)$

Divide using long division. State the quotient, and the remainder, $r\left(x\right)$. $(12x^2+x-4)÷(3x-2)$

Divide using long division. State the quotient, and the remainder, $r\left(x\right)$. $\frac{2x^3 + 7x^2 + 9x - 20}{x + 3}$

In Exercises 1–16, divide using long division. State the quotient, and the remainder, r(x). (3x²−2x+5)/(x−3)