10.1 Add and subtract polynomials  (Page 3/10)

$5x+2$

$z^2-5z-6$

$a^2+9a+18$

$\mathrm{-12}{p}^4$

$y^3-8y^2+2y-16$

$10-9x$

$23y^2$

$m^4+4m^3+6m^2+4m+1$

$8a^5-2a^3+1$

$5c^3+11c^2-c-8$

$3x-12$

$4y+17$

$\mathrm{-13}$

$\mathrm{-22}$

${\text{6x}}^2+9x^2$

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

$\mathrm{-12}u+4u$

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

$5a+7b$

$8y+6z$

Add: $4a,-3b,-8a$

Add: $4x,3y,-3x$

$18x-2x$

$13a-3a$

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

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

$(4y^2+10y+3)+(8y^2-6y+5)$

$(7x^2-9x+2)+(6x^2-4x+3)$

$(x^2+6x+8)+(\mathrm{-4}{x}^2+11x-9)$

$(y^2+9y+4)+(\mathrm{-2}{y}^2-5y-1)$

$(3a^2+7)+(a^2-7a-18)$

$(p^2-5p-11)+(3p^2+9)$

$(6m^2-9m-3)-(2m^2+m-5)$

$(3n^2-4n+1)-(4n^2-n-2)$

$(z^2+8z+9)-(z^2-3z+1)$

$(z^2-7z+5)-(z^2-8z+6)$

$(12s^2-15s)-(s-9)$

$(10r^2-20r)-(r-8)$

Find the difference of $\left(w^2+w-42\right)$ and $\left(w^2-10w+24\right)$

Find the difference of $\left(z^2-3z-18\right)$ and $\left(z^2+5z-20\right)$

$\text{Evaluate}8y^2-3y+2$

1. ⓐ $y=5$
2. ⓑ $y=\mathrm{-2}$
3. ⓒ $y=0$

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

1. ⓐ $y=\mathrm{-4}$
2. ⓑ $y=1$
3. ⓒ $y=0$

$\text{Evaluate}4-36x\text{when:}$

1. ⓐ $x=3$
2. ⓑ $x=0$
3. ⓒ $x=\mathrm{-1}$

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

1. ⓐ $x=\mathrm{-1}$
2. ⓑ $x=0$
3. ⓒ $x=2$

A window washer drops a squeegee from a platform $275$ feet high. The polynomial $\mathrm{-16}{t}^2+275$ gives the height of the squeegee $t$ seconds after it was dropped. Find the height after $t=4$ seconds.

A manufacturer of microwave ovens has found that the revenue received from selling microwaves at a cost of p dollars each is given by the polynomial $\mathrm{-5}{p}^2+350p.$ Find the revenue received when $p=50$ dollars.

Fuel Efficiency The fuel efficiency (in miles per gallon) of a bus going at a speed of $x$ miles per hour is given by the polynomial $-\frac{1}{160}{x}^2+\frac{1}{2}x.$ Find the fuel efficiency when $x=40\text{mph.}$

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 $x=60\text{mph.}$

Using your own words, explain the difference between a monomial, a binomial, and a trinomial.

Eloise thinks the sum $5x^2+3x^4$ is $8x^6.$ What is wrong with her reasoning?