Question

factorise x cube minus x square - 17 X - 15​

Answer 1

Please see the attachment

Answer 2

The factorization of the given expression is (x + 1)(x + 3)(x - 5).

Step-by-step explanation:

Consider the provided expression.

x³ - x²  - 17x - 15

Substitute P(x)=-1 in above and check whether x-1 is a root of the equation or not.

P(-1)= -1³ - (-1)²  - 17(-1) - 15

P(-1)= -1-1+17- 15

P(-1)= -17+17=0

Hence, x+1 is one of the root of the expression now the expression can be written as:

= (x + 1)(x² - 2x  - 15)

= (x + 1)(x² - 5x + 3x - 15)

= (x + 1)(x(x - 5) + 3(x - 5))  

=(x + 1)(x + 3)(x - 5)

x³ - x²  - 17x - 15  = (x + 1)(x + 3)(x - 5)

Hence, the factorization of the given expression is (x + 1)(x + 3)(x - 5).

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