To divide the expression [tex]\((-8a + 16) \div (a - 2)\)[/tex], follow these steps:
1. Identify the numerator and the denominator:
[tex]\[
\text{Numerator} = -8a + 16
\][/tex]
[tex]\[
\text{Denominator} = a - 2
\][/tex]
2. Consider the form of the numerator:
Notice that the numerator [tex]\(-8a + 16\)[/tex] can be factored out. First, split 16 as:
[tex]\[
-8a + 16 = -8(a - 2)
\][/tex]
3. Rewrite the original division problem using this factorization:
[tex]\[
\frac{-8(a - 2)}{a - 2}
\][/tex]
4. Cancel out the common factor in the numerator and denominator:
Since [tex]\(a - 2\)[/tex] appears in both the numerator and the denominator, they cancel out, leaving:
[tex]\[
-8
\][/tex]
So, the result of dividing [tex]\((-8a + 16) \div (a - 2)\)[/tex] is:
[tex]\[
-8
\][/tex]
Thus, the simplified result of the given expression is [tex]\(-8\)[/tex].
