Q. 154.9( 8 Votes )

# Using factor theo

Answer :

Let, f (x) = x3-3x2-9x-5

The factors of the constant term - 5 are Putting x = -1, we have

f (-1) = (-1)3 – 3 (-1)2 – 9 (-1) - 5

= -1 – 3 + 9 - 5

= 0

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

Let us now divide

f (x) = x3-3x2-9x-5 by (x + 1) to get the other factors of f (x)

Using long division method, we get

x3-3x2-9x-5 = (x + 1) (x2 - 4x 5)

x2 - 4x - 5 = x2 - 5x + x - 5

= x (x - 5) + 1 (x - 5)

= (x + 1) (x - 5)

Hence, x3+13x2+32x+20 = (x + 1) (x + 1) (x - 5)

= (x + 1)2 (x – 5)

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