Topical Revision Worksheet 4 Polynomials Student Version

Adapted from HCI Resources 1 Hwa Chong Institution Integrated Programme Secondary Three Mathematics Name: _______________________________ ( ) Class: _________ Date: _____________ Topical Revision Worksheet 4 _________________________________________________________________________________ Topic: Polynomials Question 1 [2008 EOY, Q11] marks (i) (a) Show that is a factor of . Answer: Sub : [1] (i) (b) Solve for x if . Answer: or [4] (ii) The expression leaves a remainder of when divided by . Find the values of p and q. Answer: and [5] Question 2 [2010 EOY, Q12] marks (a) Solve for x when . Answer: or [3] (b) It is given that where is a polynomial. (i) State the degree of . Answer: Degree of is 1 as it is linear [1] (ii) Find the values of a and b. Answer: and [3] Question 3 [2011 EOY, Q11] marks (i) Given that has a factor and the other two roots of the equation are and . Find the value of and of . Answer: , [4] (ii) Solve the equation . Answer: [4]

Adapted from HCI Resources 2 Question 4 [2012 EOY, Q8] marks The cubic polynomial is such that the coefficient of is 2 and the roots of are −1, 2k and . It is given that has a remainder of 168 when divided by . (i) Show that . Answer: [3] (ii) Hence find a value for k and show that there are no other real values of k which satisfy this equation. Answer: By trial and error, k = 3 [4] (iii) Use your answer to part (ii) to solve the equation . Answer: [2] Question 5 [2013 EOY, Q5] marks Given that is a factor of , find the value of a and of b. Answer: a = 16 and b = 3 [4] Question 6 [2014 EOY, Q7] Marks (i) Solve the equation . Answer: [4] (ii) Find the remainder when is divided by . Answer: [4] Question 7 [2015 EOY, Q9] Marks (i) Solve for x when . Answer: [5] (ii) Given that , where p and q are unknown constants, leaves a remainder of 2 when divided by and a remainder of 9 when divided by , find the values of p and q and hence find the remainder when is divided by . Answer: and , [6]