The polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).
The given polynomial to us is p(x) = x³ + 5x² - x - 5.
We are asked to factor the polynomial by grouping.
We can do this by following these steps:
- p(x) = x³ + 5x² - x - 5.
- We group the first two terms and the next two terms to get p(x) = (x³ + 5x²) + (-x -5).
- Now, we take x² common from the first group and -1 common from the second group to get p(x) = x²(x + 5) -1(x + 5)
- Now, we take (x + 5) common from both the terms to get, p(x) = (x + 5)(x² - 1).
- Now, we right (x² - 1) as (x + 1)(x - 1). to get the polynomial as, p(x) = (x + 5)(x + 1)(x - 1).
Therefore, the polynomial p(x) = x³ + 5x² - x - 5, can be factored and grouped and be written as p(x) = (x + 5)(x + 1)(x - 1).
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