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).
What is the expression in factored form?
6x^5+3x^3−9x^2
show steps
3 answers
don't stop there.
3x^2(2x^3 + x − 3) = 3x^2 (x-1)(2x^2+2x+3)
3x^2(2x^3 + x − 3) = 3x^2 (x-1)(2x^2+2x+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).
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).