1.

Factorise `y^2-5y+6`by using the Factor Theorem.

Answer» Here, we have to factorise `P(y) = y^2 - 5y +6`
Now,`(y-a)(y-b) = y^2 - by - ay + ab`Comparing above expression with given equation,
`ab = 6`
So,possible values are `(1,6),(-1,-6),(2,3),(-2,-3)`.
So, possibilities are `+-1,+-2,+-3,+-6`
Now, from Factor theoram,
`(y-a)` is a factor of `P(y) if P(a) = 0`
Now, we can check P(y) for all possible values.
`P(1) = 1-5+6 = 2`
`P(2) = 4-10+6 = 0`
`P(3) = 9-15+6 = 0`
`P(6) = 36-30+6 = 12`
So, only `P(2)` and `P(3)` are `0` as all negative values results in positive values of `P(y)`.
So, factor of `P(y) = (y-2)(y-3)`


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