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Section 1
Add and Subtract Polynomials
Determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.(a) $81 b^{5}-24 b^{3}+1$(b) $5 c^{3}+11 c^{2}-c-8 $(c) $\frac{14}{15} y+\frac{1}{7}$(d) 5(e) $4 y+17$
Determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.(a) $x^{2}-y^{2}$(b) $-13 c^{4}$(c) $x^{2}+5 x-7$ (1) (d) $x^{2} y^{2}-2 x y+8$(e) 19
Determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.(a) $8-3 x$(b) $z^{2}-5 z-6$(c) $y^{3}-8 y^{2}+2 y-16$(d) $81 b^{5}-24 b^{3}+1$ (e) -18
Determine if each of the following polynomials is a monomial, binomial, trinomial, or other polynomial.(a) $11 y^{2}$ (b) -73(c) $6 x^{2}-3 x y+4 x-2 y+y^{2}$(d) $4 y+17$ (e) $5 c^{3}+11 c^{2}-c-8$
Determine the degree of each polynomial.(a) $6 a^{2}+12 a+14$ (b) $18 x y^{2} z$(c) $5 x+2$(d) $y^{3}-8 y^{2}+2 y-16$ (e) -24
Determine the degree of each polynomial.(a) $9 y^{3}-10 y^{2}+2 y-6$(b) $-12 p^{4} \quad$ (c) $a^{2}+9 a+18$(d) $20 x^{2} y^{2}-10 a^{2} b^{2}+30 (e) $17$
Determine the degree of each polynomial.(a) $14-29 x$ (b) $z^{2}-5 z-6$ (c) $y^{3}-8 y^{2}+2 y-16$(d)$23 a b^{2}-14$ (e) -3
Determine the degree of each polynomial.(a) $62 y^{2}$(b) 15(c) $6 x^{2}-3 x y+4 x-2 y+y^{2}$(d) $10-9 x$(e) $n^{4}+4 m^{3}+6 m^{2}+4 m+1$
Add or subtract the monomials.$$7 x^{2}+5 x^{2}$$
Add or subtract the monomials.$$4 y^{3}+6 y^{3}$$
Add or subtract the monomials.$$-12 w+18 w$$
Add or subtract the monomials.$$-3 m+9 m$$
Add or subtract the monomials.$$4 a-9 a$$
Add or subtract the monomials.$$-y-5 y$$
Add or subtract the monomials.$$28 x-(-12 x)$$
Add or subtract the monomials.$$13 z-(-4 z)$$
Add or subtract the monomials.$$-5 b-17 b$$
Add or subtract the monomials.$$-10 x-35 x$$
Add or subtract the monomials.$$12 a+5 b-22 a$$
Add or subtract the monomials.$$14 x-3 y-13 x$$
Add or subtract the monomials.$$2 a^{2}+b^{2}-6 a^{2}$$
Add or subtract the monomials.$$5 u^{2}+4 v^{2}-6 u^{2}$$
Add or subtract the monomials.$$x y^{2}-5 x-5 y^{2}$$
Add or subtract the monomials.$$p q^{2}-4 p-3 q^{2}$$
Add or subtract the monomials.$$a^{2} b-4 a-5 a b^{2}$$
Add or subtract the monomials.$$x^{2} y-3 x+7 x y^{2}$$
Add or subtract the monomials.$$12 a+8 b$$
Add or subtract the monomials.$$19 y+5 z$$
Add or subtract the monomials.Add: $4 a,-3 b,-8 a$
Add or subtract the monomials.Add: $4 \mathrm{x}, 3 y,-3 x$
Add or subtract the monomials.Subtract $5 x^{6}$ from $-12 x^{6}$.
Add or subtract the monomials.Subtract $2 p^{4}$ from $-7 p^{4}$.
Add or subtract the polynomials.$$\left(5 y^{2}+12 y+4\right)+\left(6 y^{2}-8 y+7\right)$$
Add or subtract the polynomials.$$\left(4 y^{2}+10 y+3\right)+\left(8 y^{2}-6 y+5\right)$$
Add or subtract the polynomials.$$\left(x^{2}+6 x+8\right)+\left(-4 x^{2}+11 x-9\right)$$
Add or subtract the polynomials.$$\left(y^{2}+9 y+4\right)+\left(-2 y^{2}-5 y-1\right)$$
Add or subtract the polynomials.$$\left(8 x^{2}-5 x+2\right)+\left(3 x^{2}+3\right)$$
Add or subtract the polynomials.$$\left(7 x^{2}-9 x+2\right)+\left(6 x^{2}-4\right)$$
Add or subtract the polynomials.$$\left(5 a^{2}+8\right)+\left(a^{2}-4 a-9\right)$$
Add or subtract the polynomials.$$\left(p^{2}-6 p-18\right)+\left(2 p^{2}+11\right)$$
Add or subtract the polynomials.$$\left(4 m^{2}-6 m-3\right)-\left(2 m^{2}+m-7\right)$$
Add or subtract the polynomials.$$\left(3 b^{2}-4 b+1\right)-\left(5 b^{2}-b-2\right)$$
Add or subtract the polynomials.$$\left(a^{2}+8 a+5\right)-\left(a^{2}-3 a+2\right)$$
Add or subtract the polynomials.$$\left(b^{2}-7 b+5\right)-\left(b^{2}-2 b+9\right)$$
Add or subtract the polynomials.$$\left(12 s^{2}-15 s\right)-(s-9)$$
Add or subtract the polynomials.$$\left(10 r^{2}-20 r\right)-(r-8)$$
Subtract $\left(9 x^{2}+2\right)$ from $\left(12 x^{2}-x+6\right)$.
Subtract $\left(5 y^{2}-y+12\right)$ from $\left(10 y^{2}-8 y-20\right)$.
Subtract $\left(7 w^{2}-4 w+2\right)$ from $\left(8 w^{2}-w+6\right)$.
Subtract $\left(5 x^{2}-x+12\right)$ from $\left(9 x^{2}-6 x-20\right)$.
Find the sum of $\left(2 p^{3}-8\right)$ and $\left(p^{2}+9 p+18\right)$.
Find the sum of $\left(q^{2}+4 q+13\right)$ and $\left(7 q^{3}-3\right)$.
Find the sum of $\left(8 a^{3}-8 a\right)$ and $\left(a^{2}+6 a+12\right)$.
Find the sum of $\left(b^{2}+5 b+13\right)$ and $\left(4 b^{3}-6\right)$.
Find the difference of $\left(w^{2}+w-42\right)$ and $\left(w^{2}-10 w+24\right)$.
Find the difference of $\left(z^{2}-3 z-18\right)$ and $\left(z^{2}+5 z-20\right)$.
Find the difference of $\left(c^{2}+4 c-33\right)$ and $\left(c^{2}-8 c+12\right)$.
Find the difference of $\left(t^{2}-5 t-15\right)$ and $\left(t^{2}+4 t-17\right)$.
Add or subtract the polynomials.$$\left(7 x^{2}-2 x y+6 y^{2}\right)+\left(3 x^{2}-5 x y\right)$$
Add or subtract the polynomials.$$\left(-5 x^{2}-4 x y-3 y^{2}\right)+\left(2 x^{2}-7 x y\right)$$
Add or subtract the polynomials.$$\left(7 m^{2}+m n-8 n^{2}\right)+\left(3 m^{2}+2 m n\right)$$
Add or subtract the polynomials.$$\left(2 r^{2}-3 r s-2 s^{2}\right)+\left(5 r^{2}-3 r s\right)$$
Add or subtract the polynomials.$$\left(a^{2}-b^{2}\right)-\left(a^{2}+3 a b-4 b^{2}\right)$$
Add or subtract the polynomials.$$\left(m^{2}+2 n^{2}\right)-\left(m^{2}-8 m n-n^{2}\right)$$
Add or subtract the polynomials.$$\left(u^{2}-v^{2}\right)-\left(u^{2}-4 u v-3 v^{2}\right)$$
Add or subtract the polynomials.$$\left(j^{2}-k^{2}\right)-\left(j^{2}-8 j k-5 k^{2}\right)$$
Add or subtract the polynomials.$$\left(p^{3}-3 p^{2} q\right)+\left(2 p q^{2}+4 q^{3}\right)-\left(3 p^{2} q+p q^{2}\right)$$
Add or subtract the polynomials.$$\left(a^{3}-2 a^{2} b\right)+\left(a b^{2}+b^{3}\right)-\left(3 a^{2} b+4 a b^{2}\right)$$
Add or subtract the polynomials.$$\left(x^{3}-x^{2} y\right)-\left(4 x y^{2}-y^{3}\right)+\left(3 x^{2} y-x y^{2}\right)$$
Add or subtract the polynomials.$$\left(x^{3}-2 x^{2} y\right)-\left(x y^{2}-3 y^{3}\right)-\left(x^{2} y-4 x y^{2}\right)$$
Evaluate each polynomial for the given value.Evaluate $8 y^{2}-3 y+2$ when: ? y = 5 ? y = ?2 ? y = 0
Evaluate each polynomial for the given value.Evaluate $5 y^{2}-y-7$ when: ? y = ?4 ? y = 1 ? y = 0
Evaluate each polynomial for the given value.Evaluate $4-36 x$ when: ? x = 3 ? x = 0 ? x = ?1
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 $-4 p^{2}+420 p$. 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 $-4 p^{2}+420 p$. 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 $x=30 \mathrm{mph}$.
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 $0.06 x^{2}+1.1 x$. Find the stopping distance when $x=40 \mathrm{mph}$.
Rental Cost The cost to rent a rug cleaner for $d$ days is given by the polynomial $5.50 d+25$. 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 $-16 t^{2}+60 t+90$ 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 $c=65^{\circ}$.
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 $6 y^{2}+5 y^{4}$ is $11 y^{6}$. 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?
