Question

Factorise y2

– y – 6 by using the factor theorem.​

Answer 1

ANSWER OF YOUR QUESTION

Answer 2

Here, we have to factorize P(y)=y2−5y+6

Now,(y−a)(y−b)=y2−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 theorem,

(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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