Factor out the Greatest Common Factor (GCF): 45d^3-18d^2
The answer is 9d^(2)(5d-2)
To factor out the greatest common factor (GCF) of the given expression 45d^3 - 18d^2, we need to find the largest common factor of the coefficients and variables.
Step 1: Find the GCF of the coefficients.
The coefficients in this expression are 45 and 18. The GCF of 45 and 18 is 9.
Step 2: Find the GCF of the variables.
The variables in this expression are d^3 and d^2. The GCF of d^3 and d^2 is d^2.
Step 3: Write the GCF as a common factor.
The GCF of the coefficients is 9, and the GCF of the variables is d^2. So, the GCF of the expression is 9d^2.
Step 4: Divide the expression by the GCF.
To factor out the GCF, we divide each term of the expression by 9d^2:
(45d^3)/9d^2 - (18d^2)/9d^2
Simplifying the expression, we get:
5d - 2
Therefore, the factorization of 45d^3 - 18d^2 is 9d^2(5d - 2).
To factor out the Greatest Common Factor (GCF), we need to identify the largest factor that divides evenly into both terms. In this case, the terms are 45d^3 and -18d^2.
Step 1: Identify the coefficients: The coefficient of the first term is 45, and the coefficient of the second term is -18.
Step 2: Identify the common variables: The variable in both terms is 'd'.
Step 3: Determine the highest exponent of the common variable: The higher exponent of 'd' in the two terms is 3.
Step 4: Determine the common factor: To find the GCF, we take the lowest exponent of the common variable and multiply it by the coefficient. In this case, the lowest exponent of 'd' is 2 (d^2), and the GCF is the product of the coefficient and the variable to the power of the common factor (18d^2).
Step 5: Divide each term by the GCF: Divide both terms by the GCF (18d^2):
(45d^3)/(18d^2) = (45/18)(d^3/d^2) = 5d
(-18d^2)/(18d^2) = -1
Therefore, the factored form of 45d^3 - 18d^2 is:
GCF: 18d^2
Factored form: 18d^2(5d - 1)
well, take a look
45d^3 = 9d^2 * 5d
18d^2 = 9d^2 * 2
so, what do you think?