Which is the expression that can be factored using the greatest common factor for this equation? 6p^3-12p^2+9p
A. 3(2p^3-4p^2+3p)
B. 3p(2p^2-4p+3)
c. 3p^2(2p^2-4p+3)
D. 6p(p^2-2p+9)
I believe it is B because only A and B work but B is the greatest common factor. Is this correct
Thanks
6p^3-12p^2+9p
= 3p(2p^2 - 4p + 3) , that's it, since the quadratic does not factor
To determine the expression that can be factored using the greatest common factor (GCF) for the equation 6p^3-12p^2+9p, we need to find the GCF of the terms in the expression.
Step 1: Find the GCF of the coefficients:
In this case, the coefficients are 6, -12, and 9. The GCF of these numbers is 3.
Step 2: Find the GCF of the variables:
The variable in this expression is p. Since p appears in all the terms with an exponent of at least 1, the GCF of the variables is p.
Step 3: Determine the GCF:
The GCF of the coefficients and variables is the product of the GCFs determined in Steps 1 and 2, which is 3p.
Step 4: Divide each term by the GCF:
Dividing each term 6p^3, -12p^2, and 9p by 3p, we get:
6p^3 ÷ 3p = 2p^2
-12p^2 ÷ 3p = -4p
9p ÷ 3p = 3
Putting it together, the factored expression using the GCF is: 3p(2p^2-4p+3)
So, your choice B, 3p(2p^2-4p+3), is indeed the correct expression that can be factored using the greatest common factor for the equation 6p^3-12p^2+9p.