0 Rajan@2021Guru Asked: March 19, 20212021-03-19T22:27:38+05:30 2021-03-19T22:27:38+05:30In: ICSE When divided by x−3 the polynomials x 3 −px 2 +x+6 and 2x 3 −x 2 −(p+3)x−6 leave the same remainder. Find the value of ′ p ′ 0 We have to find the value of p in the given polynomial when divided by x−3 leave the same remainder using remainder theorem ML Aggarwal Avichal Publication Factorisation chapter 6, question no 8(i) class 10factorisationicse Share Facebook 1 Answer Voted Oldest Recent MathsMentor Guru 2021-03-20T11:38:22+05:30Added an answer on March 20, 2021 at 11:38 am The Remainder is same whne (x−3) divides (x 3 −px 2 +x+6) & (2x 3 −x 2 −(p+3)x−6) ∴ Using Remainder Theorem R(3)=x 3 −px 2 +x+6 =3 3 −p(3 2 )+3+6 =27−9p+3 =36−9p R(3)=2x 3 −x 2 −(p+3)x−6 =2(3 3 )−3 2 −(p+3)3−6 =2×27−9−3p−9−6 =54−24−3p =30−3p Remainder are same ∴36−9p=30−3p 36−30=−3p+9p 6=6p 1=p 0 Reply Share Share Share on Facebook Share on Twitter Share on LinkedIn Share on WhatsApp Leave an answerLeave an answerCancel reply Featured image Select file Browse Add a Video to describe the problem better. Video type Youtube Vimeo Dailymotion Facebook Choose from here the video type. Video ID Put Video ID here: https://www.youtube.com/watch?v=sdUUx5FdySs Ex: "sdUUx5FdySs". Click on image to update the captcha. Save my name, email, and website in this browser for the next time I comment. Related Questions Speed of a boat in still water is 15 km/h. It goes 30 km upstream and returns back ... Find the values of k for which the pair of linear equations kx + 3y = k-2 and ... . Solve for x and y: 0.4x-1.5y = 6.5, 0.3x-0.2y=0.9. Solve graphically the system of linear equations 4x-5y +16=0 and 2x+y-6 = 0. Determine the vertices of the ... If the remainder on division of x3 + 2x2 + kx +3 by x – 3 is 21, ...

The Remainder is same whne (x−3) divides (x

3

−px

2

+x+6) & (2x

3

−x

2

−(p+3)x−6)

∴ Using Remainder Theorem

R(3)=x

3

−px

2

+x+6

=3

3

−p(3

2

)+3+6

=27−9p+3

=36−9p

R(3)=2x

3

−x

2

−(p+3)x−6

=2(3

3

)−3

2

−(p+3)3−6

=2×27−9−3p−9−6

=54−24−3p

=30−3p

Remainder are same

∴36−9p=30−3p

36−30=−3p+9p

6=6p

1=p