Factor the high-degree polynomial 6x^3+10x^2-9x-15 by grouping
To factor the given polynomial by grouping, follow these steps:
Step 1: Group the terms in pairs.
(6x^3 + 10x^2) + (-9x - 15)
Step 2: Factor out the greatest common factor (GCF) from each group.
2x^2(3x + 5) - 3(3x + 5)
Step 3: Notice that (3x + 5) is common to both terms. Factor it out.
(2x^2 - 3)(3x + 5)
Therefore, the factored form of the polynomial 6x^3 + 10x^2 - 9x - 15 is (2x^2 - 3)(3x + 5).
To factor the polynomial 6x^3 + 10x^2 - 9x - 15 by grouping, we can group the terms and factor out the greatest common factor.
The first two terms, 6x^3 + 10x^2, have a common factor of 2x^2. Factoring out 2x^2 gives us:
2x^2(3x + 5)
The last two terms, -9x - 15, have a common factor of -3. Factoring out -3 gives us:
-3(3x + 5)
Now we can see that the terms in parentheses, (3x + 5), are the same in both groupings. We can factor it out to get the final factored form:
2x^2(3x + 5) - 3(3x + 5)
This can be further simplified as:
(2x^2 - 3)(3x + 5)
To factor the high-degree polynomial 6x^3 + 10x^2 - 9x - 15 by grouping, follow these steps:
Step 1: Group the terms
First, group the terms in pairs. In this case, you can group the first two terms and the last two terms together:
(6x^3 + 10x^2) + (-9x - 15)
Step 2: Factor out the greatest common factor (GCF)
For each group, find the GCF and factor it out. In the first group, the GCF is 2x^2, and in the second group, the GCF is -3:
2x^2(3x + 5) - 3(3x + 5)
Step 3: Factor out the common binomial
Now, you can notice that the two groups have a common binomial, (3x + 5). Factor out this common binomial:
(2x^2 - 3)(3x + 5)
Therefore, the factored form of the polynomial 6x^3 + 10x^2 - 9x - 15 is (2x^2 - 3)(3x + 5).