Using factor theorem, factorize each of the following polynomial:

Question

Using factor theorem, factorize each of the following polynomial: y 3 -2 y 2 -29 y -42

Philoid · Accepted 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)