문자와 식 전체 문제

A helicopter flying at an altitude of 1000 feet drops a rescue package. The polynomial $-16{t}^{2}+1000$ gives the height of the package $t$ seconds a after it was dropped. Find the height when $t=6$ seconds.

Area of a rectangle The area of a rectangle with length 6 less than the width is given by the expression ${w}^{2}-6w$, where $w=$ width. Factor the greatest common factor from the polynomial.

Height of a baseball The height of a baseball t seconds after it is hit is given by the expression $-16{t}^{2}+80t+4$. Factor the greatest common factor from the polynomial.

Height of a toy rocket The height of a toy rocket launched with an initial speed of 80 feet per second from the balcony of an apartment building is related to the number of seconds, t, since it is launched by the trinomial $-16{t}^{2}+80t+96$. Completely factor the trinomial.

Height of a beach ball The height of a beach ball tossed up with an initial speed of 12 feet per second from a height of 4 feet is related to the number of seconds, t, since it is tossed by the trinomial $-16{t}^{2}+12t+4$. Completely factor the trinomial.

Landscaping Sue and Alan are planning to put a 15 foot square swimming pool in their backyard. They will surround the pool with a tiled deck, the same width on all sides. If the width of the deck is w, the total area of the pool and deck is given by the trinomial $4{w}^{2}+60w+225$. Factor the trinomial.

Home repair The height a twelve foot ladder can reach up the side of a building if the ladder’s base is b feet from the building is the square root of the binomial $144-{b}^{2}$. Factor the binomial.

Watermelon drop A springtime tradition at the University of California San Diego is the Watermelon Drop, where a watermelon is dropped from the seventh story of Urey Hall.

• ⓐ The binomial $-16{t}^{2}+80$ gives the height of the watermelon $t$ seconds after it is dropped. Factor the greatest common factor from this binomial.
• ⓑ If the watermelon is thrown down with initial velocity 8 feet per second, its height after $t$ seconds is given by the trinomial $-16{t}^{2}-8t+80$. Completely factor this trinomial.

Pumpkin drop A fall tradition at the University of California San Diego is the Pumpkin Drop, where a pumpkin is dropped from the eleventh story of Tioga Hall.

• ⓐ The binomial $-16{t}^{2}+128$ gives the height of the pumpkin t seconds after it is dropped. Factor the greatest common factor from this binomial.
• ⓑ If the pumpkin is thrown down with initial velocity 32 feet per second, its height after $t$ seconds is given by the trinomial $-16{t}^{2}-32t+128$. Completely factor this trinomial.

The area of a rectangular shaped patio $400$ square feet. The length of the patio is $9$ feet more than its width. Find the length and width.

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 place mat.