Question

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Answer 1

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Let's check which polynomial is divisible by ( x - 1 ) using hit , trial and error method .

A ( x ) = 3x³ + 2x² - x

The word " divisible " itself says that " it is a factor "

Using factor theorem ;

Let;

=> x - 1 = 0

=> x = 1

Substitute the value of x in p ( x )

p ( 1 ) =

3 ( 1 )³ + 2 ( 1 )² - 1

3 ( 1 ) + 2 ( 1 ) - 1

3 + 2 - 1

5 - 1

4

This implies ;

A ( x ) is not divisible by ( x - 1 )

Similarly,

B ( x ) = 5x³ - 4x² - x

B ( 1 ) =

5 ( 1 )³ - 4 ( 1 )² - 1

5 ( 1 ) - 4 ( 1 ) - 1

5 - 4 - 1

5 - 5

0

This implies ;

B ( x ) is divisible by ( x - 1 )

Similarly,

C ( x ) = 2x³ - 3x² + 2x - 1

C ( 1 ) =

2 ( 1 )³ - 3 ( 1 )² + 2 ( 1 ) - 1

2 ( 1 ) - 3 ( 1 ) + 2 - 1

2 - 3 + 2 - 1

4 - 4

0

This implies ;

C ( x ) is divisible by ( x - 1 )

Similarly,

D ( x ) = x³ + 2x² + 3x + 2

D ( 1 ) =

( 1 )³ + 2 ( 1 )² + 3 ( 1 ) + 2

1 + 2 + 3 + 2

8

This implies ;

D ( x ) is not divisible by ( x - 1 )

Therefore ;

B ( x ) & C ( x ) are divisible by ( x - 1 )