Q.1. Identify monomials, binomials and trinomials from the following:

1. $\frac{1}{2}a^2b^2c^2 \hspace{15pt} Monomial$
2. $7x\times{}y^2\times{}z^2 \hspace{15pt} Monomial$
3. $\frac{9x^3}{z} \hspace{15pt} Monomial$
4. $2x+5 \hspace{15pt} Binomial$
5. $\frac{a}{3}+\frac{b}{6} \hspace{15pt} Binomial$
6. $xy+yz+zx \hspace{15pt} Trinomial$
7. $\frac{x^2-2y^2+3z^2}{3} \hspace{15pt} Trinomial$
8. $8a\div{}9b-2a^2\times{}b^2 \hspace{15pt} Binomial$
9. $7x^2+\frac{2y^2+1}{5} \hspace{15pt} Trinomial$

Q.2. Write the numerical and literal coefficient of each of the following:

1. $-7x^2y \hspace{15pt} Numerical \ coefficient:-7 \hspace{5pt} Literal \ coefficient: x^2 y$
2. $\pi{}r^2 \hspace{35pt} Numerical \ coefficient:\pi \hspace{5pt} Literal \ coefficient: x^2 y$
3. $\frac{2a}{3} \hspace{45pt} Numerical \ coefficient: \frac{2}{3} \hspace{5pt} Literal \ coefficient: a$
4. $5a^2\times{}b\div{}2c \hspace{15pt} Numerical\ coefficient: \frac{5}{2} \hspace{5pt} Literal \ coefficient: a^2b\div{}2c$
5. $\frac{-7pq}{9xy} \hspace{15pt} Numerical \ coefficient: \frac{-7}{9} \hspace{5pt} Literal \ coefficient: \frac{pq}{xy}$

Q.3. In, $-\frac{3}{5}x^3y^2z$  write down the coefficient for:

$x^2$

$-yz$

$\frac{3}{5} xyz$

${-x}^2y$

1. Coefficient for $x^2\ :\ -\frac{3}{5}xy^2z$
2. Coefficient for $-yz\ \ :\ +\frac{3}{5}x^3y$
3. Coefficient for $+\frac{3}{5}xyz\ :\ -x^2y$
4. Coefficient for $-x^2y\ :\ \frac{3}{5}xyz$

Q.4. Identify the pairs of like terms:

1. $\frac{x}{2},-\frac{x}{3}\ :like\ terms\$
2. ${6a}^2bc,6ab^2c\ :unlike\ terms\$
3. $6pq,-3qx\ :unlike\ terms\$
4. $8a^2,-\frac{2}{3}a^2\ :like\ terms\$
5. $2x,2y\ :unlike\ terms$
6. ${3xy}^2p,-8py^2x\ :like\ terms$

Q.5.  Which of the following expressions are polynomials?

1. $1-x\ :polynomial$
2. $3+y+y^2\ :polynomial$
3. $z+\sqrt{z}\ :\ \ Not\ polynomial$
4. $x-\frac{1}{x}\ :Not\ polynomial\$
5. $x^3+x\sqrt{x}-x+2\ :Not\ polynomial$
6. $x^2+y^2+xy+x^2y^2\ :polynomial$
7. $5\ :polynomial$
8. $\frac{1}{3}x^3-x^4\ :polynomial$
9. $x^2+\sqrt{3}x+5\ :polynomial\$
10. ${5x}^2+6xy-7\sqrt{y}\ :Not\ polynomial\$
11. $6x^2\sqrt{y}-3xy+5\ :Not\ polynomial.$

Q.6. Write the degree of each of the following polynomials:

1. $2-x\ :degree\ 1$
2. $3-x^2+x^3\ :degree\ 3$
3. ${5x}^2-6x\ :degree\ 2$
4. ${2x}^3-8x\ :degree\ 3$
5. $1-x+x^4-{3x}^2\ :degree\ 4$
6. $z^3-z^4+{2z}^2-6\ :degree\ 4$
7. $1-y-y^2+{3y}^5\ :degree\ 5$
8. $x^2-\frac{x}{2}\ :degree\ 2$
9. $t^4-t^3+2t-{3t}^6\ :degree\ 6$
10. $5\ :degree\ 0$
11. $9-x^2\ :degree\ 2$
12. $1-x^3\ :degree\ 3$

Q.7. Write the degree of each of the following polynomials:

1. $xy+yz+zx+3xyz\ :degree\ 3$
2. $a^2+b^2+c^2-3abc\ :degree\ 3$
3. $2xy+3xy^2+{5x}^2y+{7x}^2y^2\ :degree\ 4$
4. $a^5-b^5-{2a}^3b^3\ :degree\ 6$
5. $x^2y+{xy}^2+5xy\ :degree\ 3$
6. $1+2x+5x^2y+{6yz}^2\ :degree\ 3$

Q.8.  Explain the following:

i) Find the value of   ${4x}^3-{3x}^2+5x-6, when \ x=4$

${4x}^3-3x^2+5x-6 = 4\times{}4^3-3\times{}4^2+5\times{}4-6 =90$

ii) Find the value of   $^3-8x^2+14x-7, when \ x=3$

$x^3-8x^2+14x-7= 3^3-8{\times{}3}^2+14\times{}3-7\ =-30$

Q.9. If $a=4 \ and \ b=5$, find the value of $a^3+b^3-{3a}^2b+{3ab}^2$

$a^3+b^3-{3a}^2b+{3ab}^2$
$= 4^3+5^3-{3\times{}4}^2\times{}5+{3\times{}4\times{}5}^2 = 249$
Q10. If $x=4, \ y=3 \ and \ z=-2$, find the value of
1. $x^2+y^2+z^2+2xyz = 4^2+3^2+({-2)}^2+2xyz = -19$
2. $x^3+y^3+z^3-3xyz = 4^3+3^3+{(-2)}^3-3\left(4\right)\left(3\right)(-2) = 155$