Using factor theorem, factorize each of the following polynomial:

Question

Using factor theorem, factorize each of the following polynomial: x 3 -10 x 2 -53 x -42

Philoid · Accepted Answer

Let, f (x) = x³-10x²-53x-42

The factors of the constant term – 42 are

Putting x = - 1, we have

f (-1) = (-1)³ – 10 (-1)² – 53 (-1) - 42

= -1 – 10 + 53 - 42

= 0

So, (x + 1) is a factor of f (x)

Let us now divide

f (x) = x³-10x²-53x-42 by (x + 1) to get the other factors of f (x)

Using long division method, we get

x³-10x²-53x-42 = (x + 1) (x² – 11x – 42)

x² – 11x - 42 = x² – 14x + 3x - 42

= x (x – 14) + 3 (x – 14)

= (x – 14) (x + 3)

Hence, x³-10x²-53x-42 = (x + 1) (x - 14) (x + 3)