Question

factorise y^2 - 5y + 6 by using factor theorem ​

Answer 1

Solution :

Let, f(y) = y²-5y+6

Now, (y-a)(y-b) = y²-ay-by+ab ...(1)

On comparing equation (1) to the given equation : ab = 6

so, the possible values will be :

( 1,6 ) , ( -1,-6 ) , ( 2,3, ) and ( -2,-3)

So, the possible values :

$\binom{ + }{ - } 1 \: \binom{ + }{ - } 2 \: \binom{ + }{ - } 3 \: and \: \binom{ + }{ - } 6$

Also, ( y - a ) is a factor of given polynomial , so the value of f(a) will be 0

On checking :

P(1) = (1)² - 5(1) + 6 = 2

P(2) = (2)² - 5(2) + 6 = 0

P(3) = (3)² - 5(3) + 6 = 0

P(6) = (6)² - 5(6) + 6 = 12

thus the possible values are 2 and 3

So, the factors of polynomial f(y) will be (y-2) and (y-3)

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