THIS IS A TEST EXSPLAIN HOW YOU GOT THE ANSWER without *{}|?/

Question

Factor the expression completely.

45x−18y+36

(1 point)

Answer 1

To factor the expression \( 45x - 18y + 36 \) completely, follow these steps:

1. Identify the Greatest Common Factor (GCF): Look for the GCF of the coefficients in the expression. The coefficients are \( 45 \), \( -18 \), and \( 36 \).

   • The factors of \( 45 \) are \( 1, 3, 5, 9, 15, 45 \).
   • The factors of \( -18 \) are \( 1, 2, 3, 6, 9, 18 \).
   • The factors of \( 36 \) are \( 1, 2, 3, 4, 6, 9, 12, 18, 36 \).
   • The GCF of these three numbers is \( 9 \).

2. Factor out the GCF: Divide each term in the expression by the GCF \( 9 \):

   • \( 45x \div 9 = 5x \)
   • \( -18y \div 9 = -2y \)
   • \( 36 \div 9 = 4 \)

   Therefore, we can factor out \( 9 \) from the expression: \[ 45x - 18y + 36 = 9(5x - 2y + 4) \]

3. Check if the Remaining Expression Can Be Factored: Now, we need to check if \( 5x - 2y + 4 \) can be factored further. To check if this trinomial can be factored, look for two numbers that multiply to \( 5 \times 4 = 20 \) and add to \( -2 \).

   However, there are no such integers, hence \( 5x - 2y + 4 \) does not factor further.

4. Final Factored Form: The completely factored form of the expression is: \[ 9(5x - 2y + 4) \]

Thus, the answer is \( 9(5x - 2y + 4) \).

Answer 2

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Answer 3

The completely factored form of the expression 45x - 18y + 36 is 9(5x - 2y + 4).