Topical Revision Paper 4 Unit 4 Ploynomials Students

Topical Revision Paper 4 Term 2 Unit 4: Polynomials Question 1: It is given that f( ) ( 3)(2 1)g( )x x x x mx c     , where f( )x and g( )x are polynomials in terms of x, and m and c are constants. The polynomial f( )x has a remainder of 11 when divided by ( 3)x , and a remainder of 4 when divided by (2 1)x . (i) Find the value of m and of c . [4] (ii) Hence, find the remainder when f( )x is divided by 22 5 3xx . [1] Answer: (i) 2 , 5mc  (ii) Remainder is 2 5x Question 2: (i) Factorise 32 5 3 9x x x   completely. [4] (ii) Hence, solve the equation 6 4 28 20 6 9x x x   . [3] Answer: (i) 2f( ) ( 1)( 3)x x x   (ii) 6 or 1.222xx  Question 3: The polynomial P is given by   322 7 6 1P x x x x    . (i) Verify that 1 2x is a root of the equation   0Px  . [1] (ii) Express  Px in the form    221x Ax Bx C   where A , B and C are constants to be determined. [2] (iii) Find the remaining roots of   0Px  using completing square method, expressing your answer in exact form. [3] (iv) Hence solve the equation 232 7e 6e e 0x x x    . [3] Answer : (ii) A = 1, C = −1 , B = 4 (iii) 2 5 or 2 5xx    (iv) ln 2,1.44 or 0.693,1.44xx

Question 4: Using long division, find the quotient when 3212 8 2x x x   is divided by 2(2 1) .x [3] Answer : Quotient = 3x-1 Question 5: (i) Find the values of p and q for which 2 6xx is a factor of 322 17x px x q   . [4] (ii) Using the values of p and q found in part (i), solve the equation 322 17 0x px x q    . [3] (iii) Hence, sketch the graph of 322 17y x px x q    . [3] Answer : (i) 3 and 30pq  (ii) 3, 2 or 2.5x x x  