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Using factor theorem, factorize each of the following polynomials:
$y^3 - 7y + 6$
Given:
Given expression is $y^3 - 7y + 6$.
To do:
We have to find the given polynomial using factor theorem.
Solution:
Let $f(y) = y^3 - 7y + 6$
The factors of the constant term in $f(y)$ are $\pm 1, \pm 2, \pm 3$ and $\pm 6$
Let $y = 1$,this implies,
$f (1) = (1)^3 - 7 (1) + 6$
$= 1 - 7 + 6$
$= 0$
Therefore, $(y - 1)$ is a factor of $f(y)$.
Let $y = 2$,this implies,
$f (2) = (2)^3 - 7 (2) + 6$
$= 8 - 14 + 6$
$= 0$
Therefore, $(y - 2)$ is a factor of $f(y)$.
Let $y = -3$,this implies,
$f (-3) = (-3)^3 - 7 (-3) + 6$
$= -27 +21 + 6$
$= 0$
Therefore, $(y + 3)$ is a factor of $f(y)$.
Hence, $f(y)=(y-1)(y-2)(y+3)$.
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