Question 1: Identify monomials, binomials and trinomials from the following:

$\displaystyle \text{i) } \frac{1}{2} a^2b^2c^2$           $\displaystyle \text{ii) } 7x \times y^2 \times z^2$            $\displaystyle \text{iii) } \frac{9x^3}{z}$            $\displaystyle \text{iv) }2x+5$

$\displaystyle \text{v) }\frac{a}{3} + \frac{b}{6}$            $\displaystyle \text{vi) }\text{i) } xy+yz+zx$            $\displaystyle \text{vii) } \frac{x^2-2y^2+3z^2}{3}$

$\displaystyle \text{viii) } 8a\div{}9b-2a^2 \times b^2$            $\displaystyle \text{ix) } 7x^2+ \frac{2y^2+1}{5}$

$\displaystyle \text{i) } \frac{1}{2} a^2b^2c^2 \text{ is a Monomial }$

$\displaystyle \text{ii) } 7x \times y^2 \times z^2 \text{ is a Monomial }$

$\displaystyle \text{iii) } \frac{9x^3}{z} \text{ is a Monomial }$

$\displaystyle \text{iv) } 2x+5 \text{ is a Binomial }$

$\displaystyle \text{v) } \frac{a}{3} + \frac{b}{6} \text{ is a Binomial }$

$\displaystyle \text{vi) } xy+yz+zx \text{ is a Trinomial }$

$\displaystyle \text{vii) } \frac{x^2-2y^2+3z^2}{3} \text{ is a Trinomial }$

$\displaystyle \text{viii) } 8a\div{}9b-2a^2 \times b^2 \text{ is a Binomial }$

$\displaystyle \text{ix) } 7x^2+ \frac{2y^2+1}{5} \text{ is a Trinomial }$

$\displaystyle \\$

Question 2: Write the numerical and literal coefficient of each of the following:

$\displaystyle \text{i) } -7x^2y$          $\displaystyle \text{ii) } \pi{}r^2$ $\displaystyle \text{iii) } \frac{2a}{3}$          $\displaystyle \text{iv) } 5a^2 \times b \div 2c$          $\displaystyle \text{v) } \frac{-7pq}{9xy}$

$\displaystyle \text{i) } -7x^2y \text{ Numerical coefficient } : -7 \text{ Literal coefficient } : x^2 y$

$\displaystyle \text{ii) } \pi{}r^2 \text{ Numerical coefficient } : \pi \text{ Literal coefficient } : x^2 y$

$\displaystyle \text{iii) } \frac{2a}{3} \text{ Numerical coefficient } : \frac{2}{3} \text{ Literal coefficient } : a$

$\displaystyle \text{iv) } 5a^2 \times b \div 2c \text{ Numerical coefficient } : \frac{5}{2} \text{ Literal coefficient } : a^2b\div{}2c$

$\displaystyle \text{v) } \frac{-7pq}{9xy} \text{ Numerical coefficient } : \frac{-7}{9} \text{ Literal coefficient } : \frac{pq}{xy}$

$\displaystyle \\$

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

$\displaystyle \text{i) } x^2$           $\displaystyle \text{ii) } -yz$           $\displaystyle \text{iii) } \frac{3}{5} xyz$            $\displaystyle \text{ iv) } {-x}^2y$

$\displaystyle \text{i) } \text{Coefficient for } x^2 : - \frac{3}{5} xy^2z$           $\displaystyle \text{ii) } \text{Coefficient for } -yz : + \frac{3}{5} x^3y$

$\displaystyle \text{iii) } \text{Coefficient for } + \frac{3}{5} xyz : -x^2y$           $\displaystyle \text{ iv) } \text{Coefficient for } -x^2y : \frac{3}{5} xyz$

$\displaystyle \\$

Question 4: Identify the pairs of like terms:

$\displaystyle \text{i) } \frac{x}{2} ,- \frac{x}{3}$          $\displaystyle \text{ii) } {6a}^2bc,6ab^2c$          $\displaystyle \text{iii) } 6pq,-3qx$         $\displaystyle \text{ iv) } 8a^2,- \frac{2}{3} a^2$          $\displaystyle \text{ v) } 2x,2y$          $\displaystyle \text{ vi) } {3xy}^2p,-8py^2x$

$\displaystyle \text{i) } \frac{x}{2} ,- \frac{x}{3} : \text{ The two terms are like terms. }$

$\displaystyle \text{ii) } {6a}^2bc,6ab^2c : \text{ The two terms are unlike terms. }$

$\displaystyle \text{iii) } 6pq,-3qx : \text{ The two terms are unlike terms. }$

$\displaystyle \text{ iv) } 8a^2,- \frac{2}{3} a^2 : \text{ The two terms are like terms. }$

$\displaystyle \text{ v) } 2x,2y : \text{ The two terms are unlike terms. }$

$\displaystyle \text{ vi) } {3xy}^2p,-8py^2x : \text{ The two terms are like terms. }$

$\displaystyle \\$

Question 5: Which of the following expressions are polynomials?

$\displaystyle \text{i) } 1-x$           $\displaystyle \text{ii) } 3+y+y^2$          $\displaystyle \text{iii) } z+\sqrt{z}$          $\displaystyle \text{ iv) } x- \frac{1}{x}$

$\displaystyle \text{ v) } x^3+x\sqrt{x}-x+2$          $\displaystyle \text{ vi) } x^2+y^2+xy+x^2y^2$          $\displaystyle \text{ vii) } 5$

$\displaystyle \text{viii) } \frac{1}{3} x^3-x^4$          $\displaystyle \text{ix) } x^2+\sqrt{3}x+5$          $\displaystyle \text{x) } {5x}^2+6xy-7\sqrt{y}$

$\displaystyle \text{xi) } 6x^2\sqrt{y}-3xy+5$

$\displaystyle \text{i) } 1-x : \text{ Is a polynomial. }$

$\displaystyle \text{ii) } 3+y+y^2 : \text{ Is a polynomial. }$

$\displaystyle \text{iii) } z+\sqrt{z} : \text{ Is Not a polynomial. }$

$\displaystyle \text{ iv) } x- \frac{1}{x} : \text{ Is Not a polynomial. }$

$\displaystyle \text{ v) } x^3+x\sqrt{x}-x+2 : \text{ Is Not a polynomial. }$

$\displaystyle \text{ vi) } x^2+y^2+xy+x^2y^2 : \text{ Is a polynomial. }$

$\displaystyle \text{vii) } 5 : \text{ Is a polynomial. }$

$\displaystyle \text{viii) } \frac{1}{3} x^3-x^4 : \text{ Is a polynomial. }$

$\displaystyle \text{ix) } x^2+\sqrt{3}x+5 : \text{ Is a polynomial. }$

$\displaystyle \text{x) } {5x}^2+6xy-7\sqrt{y} : \text{ Is Not a polynomial. }$

$\displaystyle \text{xi) } 6x^2\sqrt{y}-3xy+5 : \text{ Is Not a polynomial. }$

$\displaystyle \\$

Question 6: Write the degree of each of the following polynomials:

$\displaystyle \text{i) } 2-x$          $\displaystyle \text{ii) } 3-x^2+x^3$          $\displaystyle \text{iii) } {5x}^2-6x$          $\displaystyle \text{ iv) } {2x}^3-8x$

$\displaystyle \text{ v) } 1-x+x^4-{3x}^2$          $\displaystyle \text{ vi) } z^3-z^4+{2z}^2-6$          $\displaystyle \text{ vii) } 1-y-y^2+{3y}^5$

$\displaystyle \text{viii) } x^2- \frac{x}{2}$           $\displaystyle \text{ix) } t^4-t^3+2t-{3t}^6$          $\displaystyle \text{x) } 5$          $\displaystyle \text{xi) } 9-x^2$          $\displaystyle \text{xii) } 1-x^3$

$\displaystyle \text{i) } 2-x : \text{ degree } 1$

$\displaystyle \text{ii) } 3-x^2+x^3 : \text{ degree } 3$

$\displaystyle \text{iii) } {5x}^2-6x : \text{ degree } 2$

i$\displaystyle \text{ iv) } {2x}^3-8x : \text{ degree } 3$

i$\displaystyle \text{ v) }1-x+x^4-{3x}^2 : \text{ degree } 4$

i$\displaystyle \text{ vi) } z^3-z^4+{2z}^2-6 : \text{ degree } 4$

i$\displaystyle \text{ vii) } 1-y-y^2+{3y}^5 : \text{ degree } 5$

$\displaystyle \text{viii) } x^2- \frac{x}{2} : \text{ degree } 2$

$\displaystyle \text{ix) } t^4-t^3+2t-{3t}^6 : \text{ degree } 6$

$\displaystyle \text{x) } 5 : \text{ degree } 0$

$\displaystyle \text{xi) } 9-x^2 : \text{ degree } 2$

$\displaystyle \text{xii) } 1-x^3 : \text{ degree } 3$

$\displaystyle \\$

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

$\displaystyle \text{i) } xy+yz+zx+3xyz$            $\displaystyle \text{ii) } a^2+b^2+c^2-3abc$

$\displaystyle \text{iii) } 2xy+3xy^2+{5x}^2y+{7x}^2y^2$             $\displaystyle \text{iv) } a^5-b^5-{2a}^3b^3$

$\displaystyle \text{v) } x^2y+{xy}^2+5xy$            $\displaystyle \text{vi) } 1+2x+5x^2y+{6yz}^2$

$\displaystyle \text{i) } xy+yz+zx+3xyz : \text{ The degree of the polynomial is } 3$

$\displaystyle \text{ii) } a^2+b^2+c^2-3abc : \text{ The degree of the polynomial is } 3$

$\displaystyle \text{iii) } 2xy+3xy^2+{5x}^2y+{7x}^2y^2 : \text{ The degree of the polynomial is } 4$

iv) $\displaystyle a^5-b^5-{2a}^3b^3 : \text{ The degree of the polynomial is } 6$

v) $\displaystyle x^2y+{xy}^2+5xy : \text{ The degree of the polynomial is } 3$

v$\displaystyle \text{i) } 1+2x+5x^2y+{6yz}^2 : \text{ The degree of the polynomial is } 3$

$\displaystyle \\$

Question 8: Explain the following:

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

$\displaystyle \text{ii) } \text{Find the value of } ^3-8x^2+14x-7 \text{ when } x=3$

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

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

$\displaystyle \text{ii) } \text{Find the value of } ^3-8x^2+14x-7 \text{ when } x=3$

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

$\displaystyle \\$

Question 9: If $\displaystyle a=4$ and $\displaystyle b=5 , \text{Find the value of } a^3+b^3-{3a}^2b+{3ab}^2$

$\displaystyle a^3+b^3-{3a}^2b+{3ab}^2 = 4^3+5^3-{3 \times 4}^2 \times 5+{3 \times 4 \times 5}^2 = 249$

$\displaystyle \\$

Question 10: If $\displaystyle x=4, y=3$ and $\displaystyle z=-2$, find the value of

$\displaystyle \text{i) } x^2+y^2+z^2+2xyz$ $\displaystyle \text{ii) } x^3+y^3+z^3-3xyz$

$\displaystyle \text{i) } x^2+y^2+z^2+2xyz = 4^2+3^2+({-2)}^2+2xyz = -19$