Question

Factor the polynomial twice. First use a common factor with a positive coefficient, and then use a common factor with a negative coefficient:

-5b^5 + 20b^4 - 25b

Answer 1

The polynomial -5b^5 + 20b^4 - 25b is first factored by taking out the common factor 5b, and then factored again by taking out a common factor with a negative coefficient, resulting in the final factored form of -5b * (b^4 - 4b^3 + 5).

Step-by-step explanation:

To factor the polynomial -5b^5 + 20b^4 - 25b, we first look for a common factor with a positive coefficient. We observe that all terms are divisible by 5b, so we factor that out:

5b * (-b^4 + 4b^3 - 5)

Next, we factor the polynomial again using a common factor with a negative coefficient. We can take out a -1 from the terms inside the parenthesis to get:

5b * (-1) * (b^4 - 4b^3 + 5)

This results in:

-5b * (b^4 - 4b^3 + 5)

Here we have shown how to factor the given polynomial by first finding a common factor with a positive coefficient and then with a negative coefficient.