What is the expression in factored form?
6x^5+3x^3−9x^2
show steps
don't stop there.
3x^2(2x^3 + x − 3) = 3x^2 (x-1)(2x^2+2x+3)
To find the expression in factored form, we need to look for the common factors in the given expression.
Step 1: Take out the greatest common factor (GCF) if it exists. In this case, we can factor out 3x^2, as it is present in every term:
3x^2(2x^3 + x − 3)
Step 2: Next, examine the trinomial within the parentheses, 2x^3 + x − 3, which can be factored further.
Step 3: Look for any possible common factors of the trinomial. In this case, there are no common factors.
Step 4: Proceed by factoring the trinomial using other factoring techniques, such as grouping, quadratic, or trial and error methods. However, in this specific example, the trinomial does not factor further using traditional factoring methods.
Thus, the factored form of the expression 6x^5 + 3x^3 − 9x^2 is 3x^2(2x^3 + x − 3).
To factor the expression 6x^5 + 3x^3 − 9x^2, we need to find the greatest common factor (GCF) among the terms.
First, let's look at the coefficients of the terms: 6, 3, and -9. The GCF among these numbers is 3. Now let's examine the variables. We have x^5, x^3, and x^2. The lowest exponent among these variables is x^2, so we can factor out x^2 as well.
Taking out the GCF, 3x^2, from each term we get:
6x^5 + 3x^3 − 9x^2 = 3x^2 * (2x^3 + x − 3)
Therefore, the expression in factored form is 3x^2(2x^3 + x − 3).
Apologies for stopping my explanation prematurely. You are correct. To fully factor the expression, we observe that the terms within the parentheses, 2x^3 + x − 3, can be written as:
2x^2 + 2x − x + 3
From here, we can use grouping to factor further:
2x(x + 1) − 1(x + 1)
Now, we have a common factor of (x + 1):
(x + 1)(2x - 1)
Therefore, the expression in fully factored form is 3x^2(x + 1)(2x - 1).