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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Updated on: 10-Oct-2022

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