단항식과 다항식의 계산

A manufacturer of stereo sound speakers has found that the revenue received from selling the speakers at a cost of p dollars each is given by the polynomial $-4{p}^{2}+420p.$ Find the revenue received when $p=60$ dollars.

A manufacturer of the latest basketball shoes has found that the revenue received from selling the shoes at a cost of p dollars each is given by the polynomial $-4{p}^{2}+420p.$ Find the revenue received when $p=90$ dollars.

Fuel Efficiency The fuel efficiency (in miles per gallon) of a car going at a speed of $x$ miles per hour is given by the polynomial $-\frac{1}{150}{x}^{2}+\frac{1}{3}x$. Find the fuel efficiency when $x=30\,\text{mph}$.

Stopping Distance The number of feet it takes for a car traveling at $x$ miles per hour to stop on dry, level concrete is given by the polynomial $0.06{x}^{2}+1.1x$. Find the stopping distance when $x=40\,\text{mph}$.

Rental Cost The cost to rent a rug cleaner for $d$ days is given by the polynomial $5.50d+25$. Find the cost to rent the cleaner for 6 days.

Height of Projectile The height (in feet) of an object projected upward is given by the polynomial $-16{t}^{2}+60t+90$ where $t$ represents time in seconds. Find the height after $t=2.5$ seconds.

Temperature Conversion The temperature in degrees Fahrenheit is given by the polynomial $\frac{9}{5}c+32$ where $c$ represents the temperature in degrees Celsius. Find the temperature in degrees Fahrenheit when $c=65^\circ .$

Using your own words, explain the difference between a monomial, a binomial, and a trinomial.

Using your own words, explain the difference between a polynomial with five terms and a polynomial with a degree of 5.

Ariana thinks the sum $6{y}^{2}+5{y}^{4}$ is $11{y}^{6}$. What is wrong with her reasoning?

Jonathan thinks that $\frac{1}{3}$ and $\frac{1}{x}$ are both monomials. What is wrong with his reasoning?

Distribute: $2(x+3).$

Combine like terms: ${x}^{2}+9x+7x+63.$

Multiply: $4(x+3).$

Multiply: $5(x+7).$

Multiply: $3(y+13).$

Multiply: $y(y-2).$

Multiply: $x(x-7).$

Multiply: $d(d-11).$

Multiply: $7x(2x+y).$