Section 1
Add and Subtract Polynomials
In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. (a) $47 x^5-17 x^2 y^3+y^2$(b) $5 c^3+11 c^2-c-8$(c) $\frac{5}{9} a b+\frac{1}{3} b$(d) 4(e) $4 p q+17$
In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. (a) $x^2-y^2$(b) $-13 c^4$(c) $a^2+2 a b-7 b^2$(d) $4 x^2 y^2-3 x y+8$(e) 19
In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. (a) $8 y-5 x$(b) $y^2-5 y z-6 z^2$(c) $y^3-8 y^2+2 y-16$(d) $81 a b^4-24 a^2 b^2+3 b$(E) -18
In the following exercises, determine if the polynomial 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) $4 y^2+17 z^2$(e) $5 c^3+11 c^2-c-8$
In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. (a) $5 a^2+12 a b-7 b^2$(b) $18 x y^2 z$(c) $5 x+2$(d) $y^3-8 y^2+2 y-16$(e) -24
In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. (a) $9 y^3-10 y^2+2 y-6$(b) $-12 p^3 q$(c) $a^2+9 a b+18 b^2$(d) $20 x^2 y^2-10 a^2 b^2+30$(e) 17
In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. (a) $14 s-29 t$(b) $z^2-5 z-6$(c) $y^3-8 y^2 z+2 y z^2-16 z^3$(d) $23 a b^2-14$(e) -3
In the following exercises, determine if the polynomial is a monomial, binomial, trinomial, or other polynomial. (a) $15 x y$(b) 15(c) $6 x^2-3 x y+4 x-2 y+y^2$(d) $10 p-9 q$(e) $m^4+4 m^3+6 m^2+4 m+1$
In the following exercises, add or subtract the monomials. (a) $7 x^2+5 x^2$(b) $4 \mathrm{a}-9 a$
In the following exercises, add or subtract the monomials. (a) $4 y^3+6 y^3$(b) $-y-5 y$
In the following exercises, add or subtract the monomials. (a) $-12 w+18 w$(b) $7 x^2 y-\left(-12 x^2 y\right)$
In the following exercises, add or subtract the monomials. (a) $-3 m+9 m$(b) $15 y z^2-\left(-8 y z^2\right)$
In the following exercises, add or subtract the monomials. $7 \mathrm{x}^2+5 x^2+4 \mathrm{a}-9 a$
In the following exercises, add or subtract the monomials. $4 y^3+6 y^3-y-5 y$
In the following exercises, add or subtract the monomials. $-12 w+18 w+7 x^2 y-\left(-12 x^2 y\right) \quad-3 m+9 m+15 y z^2-\left(-8 y z^2\right)$
In the following exercises, add or subtract the monomials. $-3 m+9 m+15 y z^2-\left(-8 y z^2\right)$
In the following exercises, add or subtract the monomials. (a) $-5 b-17 b$(b) $3 x y-(-8 x y)+5 x y$
In the following exercises, add or subtract the monomials. (a) $-10 x-35 x$(b) $17 m n^2-\left(-9 m n^2\right)+3 m n^2$
In the following exercises, add or subtract the monomials. (a) $12 a+5 b-22 a$(b) $p q^2-4 p-3 q^2$
In the following exercises, add or subtract the monomials. (a) $14 x-3 y-13 x$(b) $a^2 b-4 a-5 a b^2$
In the following exercises, add or subtract the monomials. (a) $2 a^2+b^2-6 a^2$(b) $x^2 y-3 x+7 x y^2$
In the following exercises, add or subtract the monomials. (a) $5 u^2+4 v^2-6 u^2$(b) $12 a+8 b$
In the following exercises, add or subtract the monomials. (a) $x y^2-5 x-5 y^2$(b) $19 y+5 z$
In the following exercises, add or subtract the monomials. $$12 a+5 b-22 a+p q^2-4 p-3 q^2$$
In the following exercises, add or subtract the monomials. $$14 x-3 y-13 x+a^2 b-4 a-5 a b^2$$
In the following exercises, add or subtract the monomials. $$2 a^2+b^2-6 a^2+x^2 y-3 x+7 x y^2$$
In the following exercises, add or subtract the monomials. $5 u^2+4 v^2-6 u^2+12 \mathrm{a}+8 b$
In the following exercises, add or subtract the monomials. $x y^2-5 x-5 y^2+19 y+5 z$
Add: $4 a,-3 b,-8 a$
Add: $4 \mathrm{x}, 3 y,-3 x$
Subtract $5 x^6$ from $-12 x^6$
Subtract $2 p^4$ from $-7 p^4$
In the following exercises, add the polynomials. $$\left(5 y^2+12 y+4\right)+\left(6 y^2-8 y+7\right)$$
In the following exercises, add the polynomials. $$\left(4 y^2+10 y+3\right)+\left(8 y^2-6 y+5\right)$$
In the following exercises, add the polynomials. $$\left(x^2+6 x+8\right)+\left(-4 x^2+11 x-9\right)$$
In the following exercises, add the polynomials. $$\left(y^2+9 y+4\right)+\left(-2 y^2-5 y-1\right)$$
In the following exercises, add the polynomials. $\left(8 x^2-5 x+2\right)+\left(3 x^2+3\right)$
In the following exercises, add the polynomials. $\left(7 x^2-9 x+2\right)+\left(6 x^2-4\right)$
In the following exercises, add the polynomials. $\left(5 a^2+8\right)+\left(a^2-4 a-9\right)$
In the following exercises, add the polynomials. $\left(p^2-6 p-18\right)+\left(2 p^2+11\right)$
In the following exercises, subtract the polynomials. $$\left(4 m^2-6 m-3\right)-\left(2 m^2+m-7\right)$$
In the following exercises, subtract the polynomials. $$\left(3 b^2-4 b+1\right)-\left(5 b^2-b-2\right)$$
In the following exercises, subtract the polynomials. $$\left(a^2+8 a+5\right)-\left(a^2-3 a+2\right)$$
In the following exercises, subtract the polynomials. $\left(b^2-7 b+5\right)-\left(b^2-2 b+9\right)$
In the following exercises, subtract the polynomials. $\left(12 s^2-15 s\right)-(s-9)$
In the following exercises, subtract the polynomials. $\left(10 r^2-20 r\right)-(r-8)$
In the following exercises, subtract the polynomials. Subtract $\left(9 x^2+2\right)$ from $\left(12 x^2-x+6\right)$
In the following exercises, subtract the polynomials. Subtract $\left(5 y^2-y+12\right)$ from $\left(10 y^2-8 y-20\right)$
In the following exercises, subtract the polynomials. Subtract $\left(7 w^2-4 w+2\right)$ from $\left(8 w^2-w+6\right)$
In the following exercises, subtract the polynomials. Subtract $\left(5 x^2-x+12\right)$ from $\left(9 x^2-6 x-20\right)$
In the following exercises, find the difference of the polynomials. Find the difference of $\left(w^2+w-42\right)$ and $\left(w^2-10 w+24\right)$
In the following exercises, find the difference of the polynomials. Find the difference of $\left(z^2-3 z-18\right)$ and $\left(z^2+5 z-20\right)$
In the following exercises, add the polynomials. $\left(7 x^2-2 x y+6 y^2\right)+\left(3 x^2-5 x y\right)$
In the following exercises, add the polynomials. $\left(-5 x^2-4 x y-3 y^2\right)+\left(2 x^2-7 x y\right)$
In the following exercises, add the polynomials. $\left(7 m^2+m n-8 n^2\right)+\left(3 m^2+2 m n\right)$
In the following exercises, add the polynomials. $\left(2 r^2-3 r s-2 s^2\right)+\left(5 r^2-3 r s\right)$
In the following exercises, add or subtract the polynomials. $\left(a^2-b^2\right)-\left(a^2+3 a b-4 b^2\right)$
In the following exercises, add or subtract the polynomials. $\left(m^2+2 n^2\right)-\left(m^2-8 m n-n^2\right)$
In the following exercises, add or subtract the polynomials. $\left(p^3-3 p^2 q\right)+\left(2 p q^2+4 q^3\right)-\left(3 p^2 q+p q^2\right)$
In the following exercises, add or subtract the polynomials. $\left(a^3-2 a^2 b\right)+\left(a b^2+b^3\right)-\left(3 a^2 b+4 a b^2\right)$
In the following exercises, add or subtract the polynomials. $\left(x^3-x^2 y\right)-\left(4 x y^2-y^3\right)+\left(3 x^2 y-x y^2\right)$
In the following exercises, add or subtract the polynomials. $\left(x^3-2 x^2 y\right)-\left(x y^2-3 y^3\right)-\left(x^2 y-4 x y^2\right)$
In the following exercises, find the function values for each polynomial function. For the function $f(x)=8 x^2-3 x+2$, find:(a) $f(5)$ (b) $f(-2)$ (c) $f(0)$
In the following exercises, find the function values for each polynomial function. For the function $f(x)=5 x^2-x-7$, find:(a) $f(-4)$ (b) $f(1)$ (c) $f(0)$
In the following exercises, find the function values for each polynomial function. For the function $g(x)=4-36 x$, find:(a) $g(3)$ (b) $g(0)$ (c) $g(-1)$
In the following exercises, find the function values for each polynomial function. For the function $g(x)=16-36 x^2$, find:(a) $g(-1)$ (b) $g(0)$ (c) $g(2)$
A painter drops a brush from a platform 75 feet high. The polynomial function $h(t)=-16 t^2+75$ gives the height of the brush $t$ seconds after it was dropped. Find the height after $t=2$ seconds.
A girl is throwing a ball off the cliff into the ocean. The polynomial $h(t)=-16 t^2+200$ gives the height of a ball $t$ seconds after it is dropped from a 250 -foot tall cliff. Find the height after $t=3$ 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 function $R(p)=-4 p^2+420 p$. 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 $R(p)=-4 p^2+420 p$. Find the revenue received when $p=90$ dollars.
The polynomial $C(x)=6 x^2+90 x$ gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side $x$ feet and height 6 feet. Find the cost of producing a box with $x=4$ feet.
The polynomial $C(x)=6 x^2+90 x$ gives the cost, in dollars, of producing a rectangular container whose top and bottom are squares with side $x$ feet and height 4 feet. Find the cost of producing a box with $x=6$ feet.
For each function, find (a) $(f+g)(x)$ (b) $(f+g)(2)$ (c) $(f-g)(x)$(d) $(f-g)(-3)$. $f(x)=2 x^2-4 x+1$ and $g(x)=5 x^2+8 x+3$
For each function, find (a) $(f+g)(x)$ (b) $(f+g)(2)$ (c) $(f-g)(x)$(d) $(f-g)(-3)$. $f(x)=4 x^2-7 x+3$ and $g(x)=4 x^2+2 x-1$
For each function, find (a) $(f+g)(x)$ (b) $(f+g)(2)$ (c) $(f-g)(x)$(d) $(f-g)(-3)$. $f(x)=3 x^3-x^2-2 x+3$ and $g(x)=3 x^3-7 x$
For each function, find (a) $(f+g)(x)$ (b) $(f+g)(2)$ (c) $(f-g)(x)$(d) $(f-g)(-3)$. $f(x)=5 x^3-x^2+3 x+4$ and $g(x)=8 x^3-1$
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?
Is every trinomial a second degree polynomial? If not, give an example.