Question

Find the remainder when 4x ^ 3 - 3x ^ 2 + 4x - 2 is divided by (i) x + 2 (i) x + 1/2​

Answer 1

Answer:

Let p(x) = 4x³ - 3x² + 4x -2

(a)

Let x-1 = 0

x = 1

Remainder theorem,

p(1) = 4(1)³ - 3(1)² + 4(1) - 2

       = 4 - 3 + 4 -2

     =3

So, R = 3

(b)

Let x-2 = 0, x= 2

p(2) = 4(2)³ -3(2)² + 4(2) -2

       = 32 - 12 +  8 -2

      = 26

So, remainder is 26

Hope this helps!

Answer 2

Answer:

Part 1:−

x−1)

4x

3

−3x

2

+4x−2

(4x

2

+x+5

4x

3

−4x

2

−+

_____________________

x

2

+4x

x

2

−x

−+

_____________________

5x−2

5x−5

−+

_____________________

3Remainder.

Part 2:−

x−2)

4x

3

−3x

2

+4x−2

(4x

2

+5x+14

4x

3

−8x

2

−+

_____________________

5x

2

+4x

5x

2

−10x

−+

_____________________

14x−2

14x−28

−+

_____________________

26Remainder.