Question

Find all factors of polynomial
2x^3+x^2-2x-1; x+1

Answer 1

Explanation:

Solution

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given, 2x

3

+x

2

−2x−1

=x

2

(2x+1)−1(2x+1)

=(x

2

−1)(2x+1)

=(x+1)(x−1)(2x+1)

Answer 2

The polynomial 2x^3 + x^2 - 2x - 1 can be factored as (x + 1)(2x^2 - x - 1).

Explanation:

To find the factors of the polynomial 2x^3 + x^2 - 2x - 1, we can use synthetic division or long division to divide the polynomial by the factor x + 1.

Using synthetic division:

-1 | 2 1 -2 -1

| -2 1 1

___________________

2 -1 -1 0

The result of the division is 2x^2 - x - 1.

So, the polynomial 2x^3 + x^2 - 2x - 1 can be factored as (x + 1)(2x^2 - x - 1).