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Use the grouping method to factor 5x^3+15x^2-2x-6

User Craz
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Answer:

(x + 3)(5x^2 - 2)

Explanation:

To factor the expression 5x^3 + 15x^2 - 2x - 6 using the grouping method, we can follow these steps:

Step 1: Group the terms in pairs:

(5x^3 + 15x^2) + (-2x - 6)

Step 2: Factor out the greatest common factor from each pair:

Finding the greatest common factor (GCF) of (5x^3 + 15x^2):

The GCF of 5x^3 and 15x^2 is 5x^2.

Thus, we have 5x^2(x + 3)

Finding the GCF of (-2x - 6):

The GCF of -2x and -6 is -2:

Thus, we have -2(x + 3)

Combining our two terms gives us 5x^2(x + 3) - 2(x + 3)

Step 3: Notice that (x + 3) is a common factor in both terms. We can factor it out:

(x + 3)(5x^2 - 2)

So, the factored form of the expression 5x^3 + 15x^2 - 2x - 6 using the grouping method is (x + 3)(5x^2 - 2).

User Faceless
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