단항식과 다항식의 계산

The polynomial $-16{t}^{2}+250$ gives the height of a ball $t$ seconds after it is dropped from a 250-foot tall building. Find the height after $t=3$ seconds.

The polynomial $6{x}^{2}+15xy$ gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and sides of height y feet. Find the cost of producing a box with $x=4$ feet and $y=6$ feet.

The polynomial $6{x}^{2}+15xy$ gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and sides of height y feet. Find the cost of producing a box with $x=6$ feet and $y=4$ feet.

The polynomial $6{x}^{2}+15xy$ gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side x feet and sides of height y feet. Find the cost of producing a box with $x=5$ feet and $y=8$ feet.

Identify Polynomials, Monomials, Binomials, and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

ⓐ $81{b}^{5}-24{b}^{3}+1$ ⓑ $5{c}^{3}+11{c}^{2}-c-8$ ⓒ $\frac{14}{15}y+\frac{1}{7}$

ⓓ 5

ⓔ $4y+17$

Identify Polynomials, Monomials, Binomials, and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

ⓐ ${x}^{2}-{y}^{2}$ ⓑ $-13{c}^{4}$ ⓒ ${x}^{2}+5x-7$ ⓓ ${x}^{2}{y}^{2}-2xy+8$ ⓔ 19

Identify Polynomials, Monomials, Binomials, and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

ⓐ $8-3x$ ⓑ ${z}^{2}-5z-6$ ⓒ ${y}^{3}-8{y}^{2}+2y-16$ ⓓ $81{b}^{5}-24{b}^{3}+1$ ⓔ $-18$

Identify Polynomials, Monomials, Binomials, and Trinomials

In the following exercises, determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.

ⓐ $11{y}^{2}$ ⓑ $-73$ ⓒ $6{x}^{2}-3xy+4x-2y+{y}^{2}$ ⓓ $4y+17$ ⓔ $5{c}^{3}+11{c}^{2}-c-8$

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

ⓐ $6{a}^{2}+12a+14$ ⓑ $18x{y}^{2}z$ ⓒ $5x+2$ ⓓ ${y}^{3}-8{y}^{2}+2y-16$ ⓔ $-24$

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

ⓐ $9{y}^{3}-10{y}^{2}+2y-6$ ⓑ $-12{p}^{4}$ ⓒ ${a}^{2}+9a+18$ ⓓ $20{x}^{2}{y}^{2}-10{a}^{2}{b}^{2}+30$ ⓔ 17

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

ⓐ $14-29x$ ⓑ ${z}^{2}-5z-6$ ⓒ ${y}^{3}-8{y}^{2}+2y-16$ ⓓ $23a{b}^{2}-14$ ⓔ $-3$

Determine the Degree of Polynomials

In the following exercises, determine the degree of each polynomial.

ⓐ $62{y}^{2}$ ⓑ 15 ⓒ $6{x}^{2}-3xy+4x-2y+{y}^{2}$ ⓓ $10-9x$ ⓔ ${m}^{4}+4{m}^{3}+6{m}^{2}+4m+1$

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

${\,\text{7x}}^{2}+5{x}^{2}$

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

${\,\text{4y}}^{3}+6{y}^{3}$

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

$-12w+18w$

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

$-3m+9m$

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

$\text{4a}-9a$

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

$-y-5y$

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

$28x-(-12x)$

Add and Subtract Monomials

In the following exercises, add or subtract the monomials.

$13z-(-4z)$