Question

Factorize x³ - x² + ax + x - a - 1​

Answer 1

Answer:

Here's your ANSWER

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Answer 2

Question:

Factorize: x³ - x² + ax + x - a - 1

Answer:

(x - 1)(x² + a + 1)

Solution:

Here,

The given polynomial is ;

x³ - x² + ax + x - a - 1

Now,

=> x³ - x² + ax + x - a - 1

=> x³ - x² + ax - a + x - 1

=> x²(x - 1) + a(x - 1) + (x - 1)

=> (x - 1)(x² + a + 1)

Moreover,

For the zeros of the polynomial we have ;

=> (x - 1)(x² + a + 1) = 0

=> x - 1 = 0 or x² + a + 1 = 0

=> x = 1 or x² = - a - 1

=> x = 1 or x² = ± √(-a-1)

Also,

For real value of x,

=> - a - 1 ≥ 0

=> - 1 ≥ a

=> a ≤ -1

Thus,

x = 1 and x = ± √(-a-1) , where a ≤ -1