I am to factor this completely and I am stuck.
2r^3 + 8r^2 +6r
Note: x^2 is x-squared (that is, x with the superscript 2), etc.
This is a double post. The equation is r but the explanation for the squared term uses x's.
To factor the expression 2r^3 + 8r^2 + 6r completely, you can try to find the greatest common factor (GCF) of all the terms and factor it out.
First, let's identify the GCF of the terms: 2r^3, 8r^2, and 6r. The GCF is the highest power of "r" that appears in all the terms, which is "r" itself.
Now, we can factor out the GCF "r" from each term:
2r^3 + 8r^2 + 6r
= r(2r^2 + 8r + 6)
Next, we need to factor the quadratic expression 2r^2 + 8r + 6. To do so, we can look for two numbers that multiply to give 2 * 6 = 12, and add up to give 8 (the coefficient of the middle term).
The numbers that satisfy these conditions are 2 and 6. So, we can rewrite the quadratic as follows:
2r^2 + 8r + 6
= r(2r^2 + 2r + 6r + 6)
Now, we can group the terms and factor by grouping:
r(2r^2 + 2r + 6r + 6)
= r((2r^2 + 2r) + (6r + 6))
= r(2r(r + 1) + 6(r + 1))
Notice that the terms inside the parentheses now have a common factor, which is "r + 1". We can factor it out:
r(2r(r + 1) + 6(r + 1))
= r(2r + 6)(r + 1)
Therefore, the completely factored form of the expression 2r^3 + 8r^2 + 6r is r(2r + 6)(r + 1).