Question

the factors of y^2-5y+6 are

Answer 1

Answer:

Step-by-step explanation:

=>y^2-5y+6=0

=>y^2-2y-3y+6=0

=>y(y-2)-3(y-2)=0

=>(y-2)(y-3)=0

1. y-2=0

=>y=2

2. y-3=0

=>y=3

Therefore , the factors are y-2 and y-3

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Answer 2

Answer:

The answer is -

(y - 2)(y - 3)

Step-by-step explanation:

To find the factors of the polynomial given in the question

Step 1 = Factorize the polynomial $y^{2}$ - 5y + 6 using identity (x + a)(x + b) = $x^{2}$ + (a + b)x + ab

Now find the factors of the last term such that it add up to middle term's y co-efficient(-5)

(-2)[a] X (-3)[b] = +6

-2[a] + (-3)[b] = -5

So,

=  $y^{2}$ + [(-2) + (-3)]y + (-2) X (-3)

=  $y^{2}$ - 2y - 3y + (-2) X (-3)

Take common

= y(y - 2) - 3(y - 2)

Again take common

= (y - 2)(y - 3)[Factors of the polynomial  $y^{2}$ - 5y + 6]