Question

0-4 Factorise y²-5y +6​

Answer 1

Answer:

(y-2)(y-3)

Step-by-step explanation:

Given:

p(y)=y^2-5y+6p(y)=y

2

−5y+6

\textbf{To find:}To find:

\text{Factorize $p(y)$ using factor theorem}Factorize p(y) using factor theorem

\textbf{Solution:}Solution:

\textbf{Factor theorem:}Factor theorem:

\text{(x-a) is a factor of f(x) iff f(a) =0}(x-a) is a factor of f(x) iff f(a) =0

p(y)=y^2-5y+6p(y)=y

2

−5y+6

p(2)=2^2-5(2)+6p(2)=2

2

−5(2)+6

p(2)=4-10+6=0p(2)=4−10+6=0

\therefore\text{y-2 is a factor of $p(y)$}∴y-2 is a factor of p(y)

p(3)=3^2-5(3)+6p(3)=3

2

−5(3)+6

p(3)=9-15+6=0p(3)=9−15+6=0

\therefore\text{y-3 is a factor of $p(y)$}∴y-3 is a factor of p(y)

\implies\bf\,p(y)=(y-2)(y-3)

⟹p(y)=(y−2)(y−3)

Answer 2

SOL.....
=y²-3y-2y+6

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

=(y-2) (y-3)