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            

Answer:

  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:

Answer:

  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?

Answer:

  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:

Answer:

  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:

Answer:

  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    

Answer:

 {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   

Answer:

 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  

Answer:

 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    
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