# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/23) | Q#3

Question The polynomial x3 + 4×2 + ax + 2, where a is a constant, is denoted by p(x). It is given that the  remainder when p(x) is divided by (x + 1) is equal to the remainder when p(x) is divided by (x − 2).     i.       Find the value of a. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/22) | Q#7

Question The polynomial , where  and  are constants, is denoted by . It is given that   is a factor of , and that when  is divided by  the remainder is 10. i.       Find the values of a and b.    ii.       When a and b have these values, solve the equation p(x)=0. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | Oct-Nov | (P2-9709/21) | Q#7

Question The polynomial , where  and  are constants, is denoted by . It is given that   is a factor of , and that when  is divided by the remainder is 10.  i.       Find the values of a and b.    ii.       When a and b have these values, solve the equation p(x)=0. […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/23) | Q#7

Question The polynomial , where a and b are constants, is denoted by . It is given that when  is divided by  the remainder is 30, and that when  is divided by  the remainder is 18. i.       Find the values of  and .    ii.       When a and b have these values, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/22) | Q#7

Question The polynomial , where a and b are constants, is denoted by . It is given that when  is divided by  the remainder is 30, and that when  is divided by  the remainder is 18. i.       Find the values of  and .    ii.       When a and b have these values, […]

# Past Papers’ Solutions | Cambridge International Examinations (CIE) | AS & A level | Mathematics 9709 | Pure Mathematics 2 (P2-9709/02) | Year 2010 | May-Jun | (P2-9709/21) | Q#4

Question The polynomial  is denoted by . i.       Find the quotient and remainder when  is divided by .    ii.       Use the factor theorem to show that  is a factor of . Solution      i.   Hence quotient is and remainder is .    ii.   We are given that; We are […]