0 Rajan@2021Guru Asked: March 19, 20212021-03-19T22:43:24+05:30 2021-03-19T22:43:24+05:30In: ICSE Show that, (x−1) is a factor of x 3 −5x 2 −x+5 hence factories x 3 −5x 2 −x+5. 0 We have been asked to prove that, (x−1) is a factor of x3−5x2−x+5 hence factories completely Book – ML Aggarwal, Avichal Publication, Factorisation, chapter 6, Question no 11 factorisationicseml aggarwal Share Facebook 1 Answer Voted Oldest Recent MathsMentor Guru 2021-03-20T11:28:35+05:30Added an answer on March 20, 2021 at 11:28 am Let us assume, x−1=0⇒x=1 Now, substitute the value of x=1 in f(x), f(1)=13−(5×12)−1+5 =1−5−1+5 =−6+6 =0 ∴ by factor theorem, (x−1) is a factor of f(x) Now dividing f(x) by (x−1), we get x 3 −5x 2 −x+5=(x−1)(x 2 −4x−5) =(x−1)(x 2 −5x+x−5) =(x−1){x(x−5)+1(x−5)} =(x−1)(x+1)(x−5) 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 Ques (b) In the figure (ii) given below, O and O’ are centres of two circles touching each ... Question 39. (a) In the figure (i) given below, AB is a chord of the circle with centre ... Question 38(b) In the figure (ii) given below, two circles with centres C, C’ intersect at A, B ... Question 38. (a) In the figure (i) given below, two circles intersect at A, B. From a point ... Question 37. If the sides of a rectangle touch a circle, prove that the rectangle is a square.

Let us assume, x−1=0⇒x=1

Now, substitute the value of x=1 in f(x),

f(1)=13−(5×12)−1+5

=1−5−1+5

=−6+6

=0

∴ by factor theorem,

(x−1) is a factor of f(x)

Now dividing f(x) by (x−1), we get

x

3

−5x

2

−x+5=(x−1)(x

2

−4x−5)

=(x−1)(x

2

−5x+x−5)

=(x−1){x(x−5)+1(x−5)}

=(x−1)(x+1)(x−5)