Factorise y2 5y 6 by using the factor theorem

Asked by admin @ 20/08/2021 in Math viewed by 388 People

Factorise y2-5y+6 by using the factor theorem

Answered by admin @ 20/08/2021

$\textbf{Given:}$

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

$\textbf{To find:}$

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

$\textbf{Solution:}$

$\textbf{Factor theorem:}$

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

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

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

$p(2)=4-10+6=0$

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

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

$p(3)=9-15+6=0$

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

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

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