Factor completely 12x5 + 6×3 + 8x2
First, factor out the greatest common factor of the terms: 2x2
2x2(6x3 + 3x + 4)
Next, attempt to factor the quadratic expression inside the parentheses. This can be done by using the quadratic formula or by observing that it can be factored into (2x + 1)(3x + 2).
2x2(2x + 1)(3x + 2)
Therefore, the fully factored form is: 2x2(2x + 1)(3x + 2).
To factor completely 12x^5 + 6x^3 + 8x^2, let's start by factoring out the greatest common factor (GCF) among the terms. In this case, the GCF is 2x^2. Factoring out 2x^2, we have:
2x^2(6x^3 + 3x + 4)
Now let's focus on factoring the expression inside the parentheses: 6x^3 + 3x + 4. Though it may not seem immediately factorable, let's look for common factors or other patterns.
After observing the terms, it seems there is no common factor among them. Therefore, the expression cannot be factored any further using integers or rational factors. In this case, the factored form will be:
2x^2(6x^3 + 3x + 4)
So, the expression 12x^5 + 6x^3 + 8x^2 is factored completely as 2x^2(6x^3 + 3x + 4).