# Using factor theo

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)

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