Math, asked by vidu10, 1 year ago

without actual division, prove that (2x^4-6x^3+3x^2+3x-2) is exactly divisible by (x^2-3x+2)

Answers

Answered by aman099
3
Let f(x) = x4 + 2x3 -2x2 + 2x - 3

g(x) = x2 + 2x - 3

= x(x + 3) - 1(x + 3) = (x - 1) (x + 3)

Now f(x) will be exactly divisible by g(x) if it is exactly divisible by (x - 1) as well as (x + 3)

i.e. if f(1) = 0 and f ( -3) = 0

Now f(1) = 14 + 2.13 -2.12 + 2.1 - 3

= 1 + 2 - 2 + 2 - 3 = 0

=> (x - 1) is a factor of f(x)

f ( -3) = (-3)4 + 2.(-3)3 -2.(-3)2 + 2.(-3) - 3

= 81 - 54 - 18 - 6 - 3 = 0

=> (x + 3) is a factor of f(x).

=> (x - 1) (x + 3) divides f (x) exactly

Therefore, x2 + 2x - 3 is a factor of f(x)
4.0
3 votes

THANKS
4
CommentsReport
THE BRAINLIEST ANSWER!

siddhartharao77Genius

This is a Verified Answer
×
Verified Answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but Verified Answers are the finest of the finest.
Given f(x) = 2x^4 - 6x^3 + 3x^2 + 3x - 2

x^2 - 3x + 2 = x^2 - x - 2x + 2

                    = x(x - 1) -2(x - 1)

                    = (x - 1)(x - 2)


If (x - 1) and (x - 2) are the factors of f(x).Then f(x) is divisible by x^2 - 3x + 2.

if f(1) = 0 and f(2) = 0, then f(x) is exactly divisible by x^2 - 3x + 2.

f(1) = 2(1)^4 - 6(1)^3 + 3(1)^2 + 3(1) - 2

      = 2 - 6 + 3 + 3 - 2

     = 0.   -------- (1)


f(2) = 2(2)^4 - 6(2)^3 + 3(2)^2 + 3(2) - 2

      = 2(16) - 6(8) + 3(4) + 6 - 2

      = 32 - 48 + 12 + 6 - 2

      = 0.    ------- (2)


From (1) & (2), we get

f(1) = 0 and f(2) = 0.


Therefore f(x) is exactly divisible by x^2 - 3x + 2.

Read more on Brainly.in - https://brainly.in/question/2287012#readmore
Answered by Anonymous
1
Hey mate...
See the attached file..

I hope that will help you mate
#yahyaahmad#
Attachments:
Similar questions