Question

Factor each completely. 5b³-b²-40b+8

Answer 1

To factor completely the equation 5b³ - b² - 40b + 8, we can factor by grouping. The factored form is (b² - 8)(5b - 1).

Step-by-step explanation:

To factor completely the equation 5b³ - b² - 40b + 8, we can try to factor by grouping.

First, group the terms in pairs:

5b³ - b² - 40b + 8 = (5b³ - b²) + (-40b + 8)

Next, find the greatest common factor (GCF) of each pair:

5b³ - b² = b²(5b - 1)

-40b + 8 = -8(5b - 1)

Now, we can factor out the GCF from each pair:

(5b³ - b²) + (-40b + 8) = b²(5b - 1) - 8(5b - 1)

Finally, we can factor out the common binomial factor:

b²(5b - 1) - 8(5b - 1) = (b² - 8)(5b - 1)