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

 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download