[PDF] [PDF] POLYNOMIAL EXAM QUESTIONS - MadAsMaths

[PDF] POLYNOMIAL EXAM QUESTIONS - MadAsMaths

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Created by T. Madas

Created by T. Madas

POLYNOMIAL

EXAM

QUESTIONS

Created by T. Madas

Created by T. Madas

Question 1 (**)

Multiply out and simplify

()()2 22 3 1 2x x x x- - + -, writing the answer in ascending powers of x.

2 3 43 7 3 5 2x x x x- - + + -

Question 2 (**)

( )3 23 6 40f x x x x≡ - + -. a) Show that ()5x- is not a factor of ()f x. b) Find a linear factor of ()f x.

MP1-N, ( 4)x-

Created by T. Madas

Created by T. Madas

Question 3 (**)

The polynomial 3 23 2 12 8x x x- - + is denoted by ()f x. a) Use the factor theorem to show that ()2x+ is a factor of ()f x. b) Factorize ()f x fully.

C2A, ( ) ( )( )( )3 2 2 2f x x x x= - - +

Question 4 (**)

The polynomial 3 24 7x x x k+ + +, where k is a constant, is denoted by ()f x. a) Given that ()2x+ is a factor of ()f x, show that 6k=. b) Express ()f x as a product of a linear factor and a quadratic factor.

C2B, ( ) ( )()22 2 3f x x x x= + + +

Created by T. Madas

Created by T. Madas

Question 5 (**)

a) Use the factor theorem to show that ()3x+ is a factor of 3 25 2 24x x x+ - -. b) Factorize 3 25 2 24x x x+ - - fully. ( )( )( )3 2 4x x x+ - +

Question 6 (**+)

Find the coefficient of 3x in the expansion of

()()3 2 3 22 5 2 1 3 2 9 7x x x x x x- + - + - +.

3... 60 ...x+

Created by T. Madas

Created by T. Madas

Question 7 (**+)

Multiply out and simplify

( )()()2 21 1 1x x x x+ + - +, writing the answer in ascending powers of x.

2 3 51x x x+ + +

Question 8 (**+)

a) Use the factor theorem to show that ()5x- is a factor of 319 30x x- -. b) Factorize 319 30x x- - into three linear factors. ( )( )( )3 2 5x x x+ + -

Created by T. Madas

Created by T. Madas

Question 9 (**+)

( )3 25f x ax x x b≡ - - +, where a and b are constants. When ()f x is divided by ()2x- the remainder is 36. When ()f x is divided by ()2x+ the remainder is 40.

Find the value of

a and the value of b.

C2D, 1a=, 42b=

Question 10 (**+)

A cubic function is defined in terms of the constant k as ( )3 2f x x x x k≡ + - +, x??.

Given that

()x k- is a factor of ()f x determine the possible values of k.

SYN-A, 1, 0k= -

Created by T. Madas

Created by T. Madas

Question 11 (**+)

( )3 22 6f x x x kx≡ - + +, where k is a constant. a) Given that ()3x- is a factor of()f x, show that 5k= -. b) Factorize ()f x into three linear factors. c) Find the remainder when ()f x is divided by ()3x+.

C2F, ( )( )( )1 2 3x x x- + -, 24R= -

Question 12 (**+)

a) Use the factor theorem to show that ()2x+ is a factor of 3 22 3 5 6x x x+ - -. b) Factorize 3 22 3 5 6x x x+ - - into three linear factors. ( )( )( )1 2 2 3x x x+ + -

Created by T. Madas

Created by T. Madas

Question 13 (**+)

( )3 22 7 5 4f x x x x≡ - - + a) Find the remainder when ()f x is divided by ()2x+. b) Use the factor theorem to show that ()4x- is a factor of ()f x. c) Factorize ()f x completely.

C2I, 30R= -, ( )( )( )2 1 1 4x x x- + -

Created by T. Madas

Created by T. Madas

Question 14 (**+)

( )3 2f x x x ax b≡ + + +, where a and b are constants When ()f x is divided by ()2x- the remainder is 7- When ()f x is divided by ()1x+ the remainder is 32 a) Find the value of a and the value of b . b) Show that ()3x- is a factor of ()f x.

17a= -, 15b=

Created by T. Madas

Created by T. Madas

Question 15 (**+)

( )3 232 10f x px x x q≡ - - +, where p and q are constants. When ()f x is divided by ()2x- the remainder is exactly the same as when ()f x is divided by ()2 3x+.

Show clearly that

8p=.

C2J, proof

Question 16 (***)

Solve the equation

( )( )( )3 21 2 3 12x x x x x+ - - - - =.

3,27x= -

Created by T. Madas

Created by T. Madas

Question 17 (***)

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