POLYNOMIAL EXAM QUESTIONS - MadAsMaths
Created by T. Madas
POLYNOMIAL EXAM
QUESTIONS
Created by T. Madas
Created by T. Madas
Question 1 (**) Multiply out and simplify
( )( ) 2x2 - x - 3 1+ 2x - x2 ,
writing the answer in ascending powers of x .
-3 - 7x + 3x2 + 5x3 - 2x4
Question 2 (**)
f ( x) x3 - 3x2 + 6x - 40 .
a) Show that ( x - 5) is not a factor of f ( x) .
b) Find a linear factor of f ( x) .
MP1-N , (x - 4)
Created by T. Madas
Created by T. Madas
Question 3 (**)
The polynomial 3x3 - 2x2 -12x + 8 is denoted by f ( x) . a) Use the factor theorem to show that ( x + 2) is a factor of f ( x) . b) Factorize f ( x) fully. C2A , f ( x) = (3x - 2)( x - 2)( x + 2)
Question 4 (**)
The polynomial x3 + 4x2 + 7x + k , where k is a constant, is denoted by f ( x) . a) Given that ( x + 2) is a factor of f ( x) , show that k = 6 . b) Express f ( x) as a product of a linear factor and a quadratic factor.
( ) C2B , f ( x) = ( x + 2) x2 + 2x + 3
Created by T. Madas
Created by T. Madas
Question 5 (**)
a) Use the factor theorem to show that ( x + 3) is a factor of x3 + 5x2 - 2x - 24 .
b) Factorize x3 + 5x2 - 2x - 24 fully.
(x + 3)(x - 2)(x + 4)
Question 6 (**+) Find the coefficient of x3 in the expansion of
( )( ) 2x3 - 5x2 + 2x -1 3x3 + 2x2 - 9x + 7 .
... + 60x3...
Created by T. Madas
Created by T. Madas
Question 7 (**+) Multiply out and simplify
( )( ) (1+ x) 1+ x2 1- x + x2 ,
writing the answer in ascending powers of x .
1+ x2 + x3 + x5
Question 8 (**+)
a) Use the factor theorem to show that ( x - 5) is a factor of x3 -19x - 30 .
b) Factorize x3 -19x - 30 into three linear factors.
(x + 3)(x + 2)(x - 5)
Created by T. Madas
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