factor (15a squared bc squared -9a squared b to the fourth c) by finding the gcf
I think the answer is either 3abc(5ac - 3a cubed) or 3a squared bc(5c - 3b cubed) Am i on the right track?
Yes, you are on the right track! To factor the expression 15a^2bc^2 - 9a^2b^4c using the greatest common factor (GCF), you need to find the largest common factor of all the terms involved.
First, let's break down each term:
15a^2bc^2 can be broken down into:
- the greatest common factor: 3abc
- remaining factors: 5ac
Similarly, -9a^2b^4c can be broken down into:
- the greatest common factor: 3ab^2c
- remaining factors: -3b^2
Now that we have identified the GCF as 3abc, we can factor it out:
3abc(5ac - 3b^2)
So, the correct answer is 3abc(5ac - 3b^2). Well done!
Yes, you are on the right track! To factor the given expression by finding the greatest common factor (GCF), follow these steps:
Step 1: Identify the terms that are common to all the coefficients and variables.
In this case, the GCF is determined by observing the coefficient, "a," and the variables, "b" and "c."
The coefficients that are common to both terms are 15 and -9. The variables that are common to both terms are "a" and "bc."
Step 2: Determine the greatest common factor of the coefficients.
The GCF of 15 and -9 is 3. Divide each coefficient by the GCF:
15 ÷ 3 = 5
-9 ÷ 3 = -3
Step 3: Determine the greatest common factor of the variables.
The GCF of "a" and "bc" is "a." Divide each variable by the GCF:
"a squared" / "a" = "a"
"b to the fourth" / "b" = "b cubed"
"c" / "c" = 1 (canceled out)
Now you have:
3a(5ac - 3a cubed bc)
So, your factorization is correct. The factored form is 3a(5ac - 3a cubed bc). Great job!