Factor the expression completely.
45x-18y+36
(1 Point)
Responses
5(9x-2y+4)
-9(5x+2y+4)
9(5x-2y+4)
9y(5x-2y+4)
The correct factorization is 9(5x - 2y + 4).
To factor the expression 45x - 18y + 36 completely, you want to factor out the greatest common factor (GCF) from each term.
The GCF of 45, 18, and 36 is 9.
The GCF of x, y, and the constant term 36 is 1.
Factoring out the GCF, you get:
9(5x - 2y + 4)
Therefore, the completely factored expression is 9(5x - 2y + 4).
To factor the expression completely, we need to find the common factors among the terms. In this case, the expression is 45x - 18y + 36.
Step 1: Find the greatest common factor (GCF) of the coefficients (45, -18, and 36).
The GCF of 45, -18, and 36 is 9 because it is the largest number that can evenly divide 45, -18, and 36.
Step 2: Divide each term of the expression by the GCF.
45x ÷ 9 = 5x
-18y ÷ 9 = -2y
36 ÷ 9 = 4
After dividing each term by 9, the expression becomes: 5x - 2y + 4.
Step 3: Write the GCF as a coefficient in front of the factored expression.
The GCF, 9, is written as a coefficient in front of the factored expression: 9(5x - 2y + 4).
Therefore, the expression 45x - 18y + 36 can be factored completely as 9(5x - 2y + 4).