Question

Using remainder theorem factorise

2x^3 - 13x^2 + 26x - 15

Answer 1

$2 x^{3} -13x^{2}+26x-15 \\ =2 x^{3} -2 x^{2} -11 x^{2} +11x+15x-15 \\ =2 x^{2} (x-1)-11x(x-10+15(x-1) \\= (2 x^{2} -11x+15)(x-1)$
$(X-1)(2 x^{2} -6X-5X+15) \\ =(X-1)(2X-5)(X-3)$
OR,
 see the attachment 

Answer 2

Step-by-step explanation:

Let p(x) = 2x^3 – 13x^2 + 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:-

(2x^2 – 11x + 15)

∴ 2x^3 – 13x^2 + 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)