Question

2ycube-11ysquare-17y-6
Factorise

Answer 1

Answer:

2y^3 – 11y^2 + 17y – 6

try if y = + or – 1

using +1

2 – 11 + 17 – 6 is not zero

try y = – 1

– 2 – 11 – 17 – 6 is not zero

try y = + or – 2

trying y = +

16 – 44 + 34 – 6 = 0

so (y – 2) is one of the factor find other factor using synthetic division or long division

using synthetic division

2 | 2 – 11 + 17 – 6

...... + 4 – 14 + 6

________________

... 2 ...– 7 + 3 + 0

so other factor is

2y² – 7y + 3

factors of it

2y² – 6y – y + 3

= 2y(y – 3) – 1(y – 3)

= (2y – 1)(y – 3)

2y^3 – 11y^2 + 17y – 6

= (y – 2)(2y – 1)(y – 3)

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