Question

if u make it fast and correctly I'll mark u as brainliest and I'll follow u​

Answer 1

I)X=-2

p(-2)=(-2)³+4(-2)+2

p(-2)=-8-8+2

p(-2)=+2

II) x=-1/2

p(-1/2)=4(-1/2)³+3(-1/2)²+5(-1/2)

p(-1/2)=-1/2+-3/4-5/2

Answer 2

Question :-

Find the remainder ( without actual division )

a) x³ + 4x + 2 is divisible by ( x - 2 )

b) 4x³ - 3x² + 5x is divisible by ( 2x + 1 )

c) 4x³ + 5x² + 6x - 7 is divisible by ( 2x - 1 )

Answer :-

Required to find :-

• Remainder in each case

Concept used :-

• Factor theorem

• Remainder theorem

Solution :-

a)

x³ + 4x + 2 is divisible by ( x + 2 )

Answer :-

So,

Let p ( x ) = x³ + 4x + 2

( x + 2 ) is divisible with p ( x )

Let x + 2 = 0

x = - 2

Substitute this value in place of x in p ( x )

So,

p ( - 2 ) =

( - 2 )³ + 4 ( - 2 ) + 2

- 8 - 8 + 2

- 16 + 2

- 14

Hence ,

Remainder = - 14

So,

p ( x ) is not exactly divisible by ( x + 2 )

$\rule{400}{2}$

b )

4x³ - 3x² + 5x is divisible by ( 2x + 1 )

Answer :-

Let p ( x ) = 4x³ - 3x² + 5x

( 2x + 1 ) is divisible by p ( x )

So,

2x + 1 = 0

2x = - 1

x = -1/2

substitute this value of -1/2 in place of x in p(x )

So,

p ( -1/2 ) =

( -1/2 )³ - 3 ( -1/2 )² + 5 ( -1/2 )

-1/8 - 3 ( 1/4 ) - 5/2

-1/8 - 3/4 - 5/2

=> - 1 - 6 - 20 / 8

=> - 27/8

Hence,

Remainder = -27/8

$\rule{400}{2}$

c)

4x³ + 5x² + 6x - 7 is divisible by 2x - 1

Answer :-

Let ,

p ( x ) = 4x³ + 5x² + 6x - 7

( 2x - 1 ) is divisible by p ( x )

So,

2x - 1 = 0

2x = 1

x = 1/2

Substitute this value of x in p ( x )

So,

p ( 1/2 ) =

4 ( 1/2 )³ + 5 ( 1/2 )² + 6 ( 1/2 ) - 7

4 ( 1/8) + 5 ( 1/4 ) + 3 - 7

1/2 + 5/4 + 3 - 7

=> 2 + 5 + 12 - 28 / 4

=> -9/4

Hence,

Remainder = -9/4

p( x ) is not exactly divisible by ( 2x - 1 )

$\rule{400}{2}$