문자와 식 전체 문제

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$(-5{x}^{2}-4xy-3{y}^{2})+(2{x}^{2}-7xy)$

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$(7{m}^{2}+mn-8{n}^{2})+(3{m}^{2}+2mn)$

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$(2{r}^{2}-3rs-2{s}^{2})+(5{r}^{2}-3rs)$

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$({a}^{2}-{b}^{2})-({a}^{2}+3ab-4{b}^{2})$

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$({m}^{2}+2{n}^{2})-({m}^{2}-8mn-{n}^{2})$

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$({u}^{2}-{v}^{2})-({u}^{2}-4uv-3{v}^{2})$

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$({j}^{2}-{k}^{2})-({j}^{2}-8jk-5{k}^{2})$

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$({p}^{3}-3{p}^{2}q)+(2p{q}^{2}+4{q}^{3})-(3{p}^{2}q+p{q}^{2})$

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$({a}^{3}-2{a}^{2}b)+(a{b}^{2}+{b}^{3})-(3{a}^{2}b+4a{b}^{2})$

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$({x}^{3}-{x}^{2}y)-(4x{y}^{2}-{y}^{3})+(3{x}^{2}y-x{y}^{2})$

Add and Subtract Polynomials

In the following exercises, add or subtract the polynomials.

$({x}^{3}-2{x}^{2}y)-(x{y}^{2}-3{y}^{3})-({x}^{2}y-4x{y}^{2})$

Evaluate a Polynomial for a Given Value

In the following exercises, evaluate each polynomial for the given value.

Evaluate $8{y}^{2}-3y+2$ when:

ⓐ $y=5$ ⓑ $y=-2$ ⓒ $y=0$

Evaluate a Polynomial for a Given Value

In the following exercises, evaluate each polynomial for the given value.

Evaluate $5{y}^{2}-y-7$ when:

ⓐ $y=-4$ ⓑ $y=1$ ⓒ $y=0$

Evaluate a Polynomial for a Given Value

In the following exercises, evaluate each polynomial for the given value.

Evaluate $4-36x$ when:

ⓐ $x=3$ ⓑ $x=0$ ⓒ $x=-1$

Evaluate a Polynomial for a Given Value

In the following exercises, evaluate each polynomial for the given value.

Evaluate $16-36{x}^{2}$ when:

ⓐ $x=-1$ ⓑ $x=0$ ⓒ $x=2$

A painter drops a brush from a platform 75 feet high. The polynomial $-16{t}^{2}+75$ 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 cliff into the ocean. The polynomial $-16{t}^{2}+250$ gives the height of a ball $t$ seconds after it is dropped from a 250-foot tall cliff. Find the height after $t=2$ 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 $-4{p}^{2}+420p.$ 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 $x=30\,\text{mph}$.