6.1 Add and subtract polynomials  (Page 2/12)

ⓐ $81b^5-24b^3+1$
ⓑ $5c^3+11c^2-c-8$
ⓒ $\frac{14}{15}y+\frac{1}{7}$
ⓓ 5
ⓔ $4y+17$

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

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

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

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

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

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

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

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

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

$\mathrm{-12}w+18w$

$\mathrm{-3}m+9m$

$\text{4a}-9a$

$\text{−}y-5y$

$28x-(\mathrm{-12}x)$

$13z-(\mathrm{-4}z)$

$\mathrm{-5}b-17b$

$\mathrm{-10}x-35x$

$12a+5b-22a$

$\text{14x}-3y-13x$

$2a^2+b^2-6a^2$

$5u^2+4v^2-6u^2$

$x{y}^2-5x-5y^2$

$p{q}^2-4p-3q^2$

$a^{2}b-4a-5a{b}^2$

$x^{2}y-3x+7x{y}^2$

$\text{12a}+8b$

$\text{19y}+5z$

Add: $4a,\mathrm{-3}b,\mathrm{-8}a$

Add: $\text{4x},3y,\mathrm{-3}x$

Subtract $5x^6\text{from}-12x^6$ .

Subtract $2p^4\text{from}-7p^4$ .

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

ⓐ $y=5$
ⓑ $y=\mathrm{-2}$
ⓒ $y=0$

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

ⓐ $y=\mathrm{-4}$
ⓑ $y=1$
ⓒ $y=0$

Evaluate $4-36x$ when:

ⓐ $x=3$
ⓑ $x=0$
ⓒ $x=\mathrm{-1}$

Evaluate $16-36x^2$ when:

ⓐ $x=\mathrm{-1}$
ⓑ $x=0$
ⓒ $x=2$

A painter drops a brush from a platform 75 feet high. The polynomial $\mathrm{-16}{t}^2+75$ 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 $\mathrm{-16}{t}^2+250$ 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 $\mathrm{-4}{p}^2+420p.$ 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 $\mathrm{-4}{p}^2+420p.$ 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 $0.06x^2+1.1x$ . 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 $\mathrm{-16}{t}^2+60t+90$ 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 $c=65\text{°}.$

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 $6y^2+5y^4$ is $11y^6$ . 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?