Question

Division algorithm method of 3x to the power of 4 +2x+4xsquare+7divided by 3x-2​

Answer 1

Answer:

Given:

p(x)=x

4

−3x

2

+4x+5

g(x)=x

2

+1−x

Degree of q(x)= Degree of p(x)−Degree of g(x)

=4−2=2

Degree of r(x)< Degree of g(x)

Let degree of r(x)=1

Let q(x)=ax

2

+bx+c and r(x)=px+q

By division algorithm

p(x)=q(x)×g(x)+r(x)

x

4

−3x

2

+4x+5=(ax

2

+bx+c)(x

2

+1−x)+(px+q)

Comparing the coefficent of x

4

.

a=1.

Comparing the coefficent of x

3

.

−a+b=0⇒b=a⇒b=1

Comparing the coefficent of x

2

a−b+c=−3

⇒1−1+c=−3⇒c=−3

Comparing the coefficent of x.

b−c+p=4

⇒1+3+p=4

⇒p=0

Comparing the coefficent of constant term.

c+q=5

−3+q=5

q=8.

So, quotient q(x)=ax

2

+bx+c

=x

2

+x−3

and remainder r(x)=px+q

=8