An important question from factorisation chapter for board examination as it has been already asked in previous paper of 2010
Use the Remainder Theorem to factorise the following expression :
2×3 + x2 – 13x + 6.
Book – ML Aggarwal Avichal Publication Factorisation chapter 6, question 16(i)
Let f(x)=2x3+x2–13x+6
For x=2, the value of f(x) will be
f(2)=2(2)3+(2)2–13(2)+6=16+4–26+6=0
As f(2)=0, so (x–2) is a factor of f(x).
Now, performing long division we have
Thus, f(x)=(x−2)(2x2+5x–3)
=(x–2)[2x2+6x–x–3]
=(x–2)[2x(x+3)−1(x+3)]
=(x–2)[2x(x+3)−1(x+3)]
=(x–2)(2x–1)(x+3)