Question

Find the remainder when p(x) = 4x^3+8x^2 - 7x+10 is
divided by (2x - 1)
​

Answer 1

Step-by-step explanation:

Let f(x)=4x

3

−8x

2

+8x+1

q(x)=2x−1

r(x)=x+3

f(x)=g(x)×q(x)+r(x)

Degree of g(x) be 2. as degree of f(x) is 3.

∴g(x)=ax

2

+bx+c

4x

3

−8x

2

+8x+1=(ax

2

+bx+c)(2x−1)+x+3

=2ax

3

+2bx

2

+2cx−ax

2

−bx+c+x+3

=2ax

3

+(2b−a)x

2

+(2c−b+1)+(3−c)

Equating coefficient of power of x,

2a=4⇒a=

2

4

=2

2b−a=−8⇒b=−3

2c−b+1=8

⇒2c+3=7

⇒c=2

∴g(x)=2x

2

−3x+2