Using factor theorem, factorize each of the following polynomial:

Question

Using factor theorem, factorize each of the following polynomial: 2 y 3 - 5y 2 -19 y +42

Philoid · Accepted Answer

Let, f (y) = 2y³-5y²-19y+42

The factors of the constant term + 42 are

Putting y = 2, we have

f (2) = 2 (2)³ – 5 (2)² – 19 (2) + 42

= 16 – 20 - 38 + 42

= 0

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

Let us now divide

f (y) = 2y³-5y²-19y+42 by (y - 2) to get the other factors of f (x)

Using long division method, we get

2y³-5y²-19y+42 = (y - 2) (2y² – y – 21)

2y² – y - 21 = (y + 3) (2y – 7)

Hence, 2y³-5y²-19y+42 = (y - 2) (2y - 7) (y + 3)