다항식 전체 문제

For the following exercises, use the given volume of a box and its length and width to express the height of the box algebraically.

Volume is $10{x}^{3}+27{x}^{2}+2x-24,$ length is $5x-4,$ width is $2x+3.$

Average cost Pictures Plus produces digital albums. The company’s average cost (in dollars) to make $x$ albums is given by the expression $\frac{7x+500}{x}$.

• ⓐ Find the quotient by dividing the numerator by the denominator.
• ⓑ What will the average cost (in dollars) be to produce 20 albums?

The polynomial function $h(t)=-16{t}^{2}+250$ gives the height of a ball t seconds after it is dropped from a 250-foot tall building. Find the height after $t=2$ seconds.

The polynomial function $h(t)=-16{t}^{2}+150$ gives the height of a stone t seconds after it is dropped from a 150-foot tall cliff. Find the height after $t=0$ seconds (the initial height of the object).

The polynomial function $h(t)=-16{t}^{2}+175$ gives the height of a ball t seconds after it is dropped from a 175-foot tall bridge. Find the height after $t=3$ seconds.

A painter drops a brush from a platform 75 feet high. The polynomial function $h(t)=-16{t}^{2}+75$ gives the height of the brush t seconds after it was dropped. Find the height after $t=2$ seconds.

A girl drops a ball off a 200-foot cliff into the ocean. The polynomial $h(t)=-16{t}^{2}+200$ gives the height of the ball, in feet, t seconds after it is dropped. Find the height after $t=3$ seconds.

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 function $R(p)=-4{p}^{2}+420p.$ 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 $R(p)=-4{p}^{2}+420p.$ Find the revenue received when $p=90$ dollars.

The polynomial $C(x)=6{x}^{2}+90x$ gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and height 6 feet. Find the cost of producing a box with $x=4$ feet.

The polynomial $C(x)=6{x}^{2}+90x$ gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and height 4 feet. Find the cost of producing a box with $x=6$ feet.

Is every trinomial a second degree polynomial? If not, give an example.

A pair of glasses is dropped off a bridge 640 feet above a river. The polynomial function $h(t)=-16{t}^{2}+640$ gives the height of the glasses t seconds after they were dropped. Find the height of the glasses when $t=6.$

A manufacturer of the latest soccer shoes has found that the revenue received from selling the shoes at a cost of $p$ dollars each is given by the polynomial $R(p)=-5{p}^{2}+360p.$ Find the revenue received when $p=10$ dollars.

A hiker drops a pebble from a bridge 240 feet above a canyon. The function $h(t)=-16{t}^{2}+240$ gives the height of the pebble $t$ seconds after it was dropped. Find the height when $t=3.$

The area of a rectangular shaped patio 432 square feet. The length of the patio is 6 feet more than its width. Find the length and width.

A ladder leans against the wall of a building. The length of the ladder is 9 feet longer than the distance of the bottom of the ladder from the building. The distance of the top of the ladder reaches up the side of the building is 7 feet longer than the distance of the bottom of the ladder from the building. Find the lengths of all three sides of the triangle formed by the ladder leaning against the building.

Shruti is going to throw a ball from the top of a cliff. When she throws the ball from 80 feet above the ground, the function $h(t)=-16{t}^{2}+64t+80$ models the height, h, of the ball above the ground as a function of time, t. Find: ⓐ the zeros of this function which tells us when the ball will hit the ground. ⓑ the time(s) the ball will be 80 feet above the ground. ⓒ the height the ball will be at $t=2$ seconds which is when the ball will be at its highest point.

The area of a rectangular place mat is 168 square inches. Its length is two inches longer than the width. Find the length and width of the placemat.

Jing is going to throw a ball from the balcony of her condo. When she throws the ball from 80 feet above the ground, the function $h(t)=-16{t}^{2}+64t+80$ models the height, h, of the ball above the ground as a function of time, t. Find: ⓐ the zeros of this function which tells us when the ball will hit the ground. ⓑ the time(s) the ball will be 128 feet above the ground. ⓒ the height the ball will be at $t=4$ seconds.