Question

laine correctly factors the expression 16.5a - 7.2b + 36. give two possible answers laine could have written.

Explanation:

Step1: Find a common factor (e.g., 0.3)

First, identify a common factor of the coefficients \(16.5\), \(-7.2\), and \(36\). Let's take \(0.3\) as a common factor.
Divide each term by \(0.3\):
\(16.5\div0.3 = 55\), \(-7.2\div0.3=-24\), \(36\div0.3 = 120\)
So, \(16.5a - 7.2b + 36=0.3(55a - 24b + 120)\)

Step2: Find another common factor (e.g., 3)

Now, take \(3\) as a common factor.
Divide each term by \(3\):
\(16.5\div3 = 5.5\), \(-7.2\div3=-2.4\), \(36\div3 = 12\)
So, \(16.5a - 7.2b + 36 = 3(5.5a - 2.4b + 12)\)

Answer:

Two possible answers are \(0.3(55a - 24b + 120)\) and \(3(5.5a - 2.4b + 12)\) (other valid common factors can be used to get different factorizations as well).