Question

using remaider theorem factorise :2x3-13x2+26x-15

Answer 1

2*3-13*2+26*-15
=6-26-390
=-20-390
=-410

Answer 2

Let p(x) = 2x3 – 13x2 + 26x – 15
Put x = 1 in p(x), we get
p(1) = 0
Hence (x – 1) is factor of p(x)
On dividing p(x) with (x – 1), we get the quotient as (2x2 – 11x + 15)
∴ 2x3 – 13x2 + 26x – 15 = (x – 1)(2x2 – 11x + 15)
   = (x – 1)(2x2 – 6x – 5x + 15)
     = (x – 1)[2x(x – 3) – 5(x – 3)]
     = (x – 1)(x – 3)(2x – 5)

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