Question

factorise :-
${ \tt {x}^{3} - 3{x}^{2} - 9x - 5}$
by long division method.
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Answer 1

Answer:

Factorize the equation: x3 – 3x2 – 9x – 5.

We will find the factors of the expression x3 – 3x2 – 9x – 5

Answer: x3 – 3x2 – 9x – 5 = (x+1)2 (x+5)

We will find one of the zeros of the expression x3 – 3x2 – 9x – 5 and use long division to find the other zeros.

Explanation:

Substitute 5 for x in x3 – 3x2 – 9x – 5

53 – 3(5)2 – 9(5) – 5 = 125 - 75 - 45 - 5 = 0

So, 5 is zero of the expression x3 – 3x2 – 9x – 5

This means (x - 5) is a factor of x3 – 3x2 – 9x – 5

Divide x3 – 3x2 – 9x – 5 by x - 5

Factorization of x3 – 3x2 – 9x – 5

This means x3 – 3x2 – 9x – 5 = (x - 5) (x2 + 2x + 1) = (x - 5) (x+1)2

Therefore, he factorization of x3 – 3x2 – 9x – 5 is (x - 5) (x+1)2

Answer 2

Answer:

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