Factors of Polynomials (CIE IGCSE Additional Maths)

The polynomial , where  and  are integers, has a factor of  .
Given that , find the values of  and .

Using your values of  and ,

find the remainder when  is divided by

factorise .

has a factor of . When  is divided by  the remainder is 105.

Find the value of and of .

Using your values of  and , write  as a product of  and a quadratic factor.

Hence solve= 0.

, where  and  are integers.

has a remainder of 11 when divided by  and a remainder of  when divided by .
Given that , find , a quadratic factor with numerical coefficients.

Hence solve .

The three roots of , where  are and , where  and  are integers. The -intercept of the graph of  is 4. Find , simplifying your coefficients.

The polynomial , where  and  are constants, has a factor of . The polynomial has a remainder of 66 when divided by .

Find the value of  and of .

Using your values of  and , show that , where  is a quadratic factor to be found.

Hence show that the equation  has only one real solution.

Find the value of .

Write  as the product of three linear factors and hence solve .

The polynomial , where  and  are constants, has a factor  and is such that .

Show that , where ,  and  are integers to be found.

Hence factorise .

Find the remainder when  is divided by.