Question

if sum of remainder obtained by dividing ax3-3ax2+7x+5 by(x-1) and(x+1) is -36 the find a​

Answer 1

Answer:

We have x

3

−ax

2

+6x−a

Apply remainder theorem

x−a=0

x=a

Put x=a in equation.

(a)

3

−a(a)

2

+6a−a

=a

3

−a

3

+6a−a

=6a−a

=5a

Then reminder is 5a

Answer 2

It is given that a polynomial ax 3 −3x 2 +4 when divided by (x−2) leaves the remainder p. Let us substitute x=2 in ax 3 −3x 2 +4 and equate it to p as follows:

a(2) 3 −3(2) 2 +4=p

⇒(a×8)−(3×4)+4=p

⇒8a−12+4=p

⇒8a−8=p....(1)

Similarly, given a polynomial 2x 3 −5x+a when divided by (x−2) leaves the remainder q. Let us substitute x=2 in 2x 3 −5x+a and equate it to q as follows:

2(2) 3 −(5×2)+a=q

⇒(2×8)−10+a=q

⇒16−10+a=q

⇒6+a=q....(2)

It is also given that p−2q=4, we, now substitute the values of p and q from equations 1 and 2 as shown below:

p−2q=4

⇒8a−8−2(6+a)=4

⇒8a−8−12−2a=4

⇒6a−20=4

⇒6a=4+20

⇒6a=24

⇒a=

6

24

⇒a=4

Hence, a=4.