Q. 124.0( 6 Votes )

Using factor theorem, factorize each of the following polynomial:

y3-2y2-29y-42

Answer :

Let, f (y) = y3-2y2-29y-42

The factors of the constant term – 42 are


Putting y = - 2, we have


f (-2) = (-2)3 – 2 (-2)2 – 29 (-2) - 42


= - 8 – 8 + 58 - 42


= 0


So, (y + 2) is a factor of f (y)


Let us now divide


f (y) = y3-2y2-29y-42 by (y + 2) to get the other factors of f (x)


Using long division method, we get


y3 - 2y2- 29y - 42 = (y + 2) (y2 – 4y – 21)


y2 – 4y - 21 = y2 – 7y + 3y - 21


= y (y – 7) + 3 (y – 7)


= (y – 7) (y + 3)


Hence, y3-2y2-29y-42 = (y + 2) (y - 7) (y + 3)


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