Question

factor completely.
$v^{2} - 10v + 16$

Explanation:

Step1: Find two numbers that multiply to 16 and add to -10.

We need two numbers \(a\) and \(b\) such that \(a\times b = 16\) and \(a + b=- 10\). The numbers are \(-2\) and \(-8\) since \((-2)\times(-8)=16\) and \((-2)+(-8)=-10\).

Step2: Rewrite the middle term using these numbers.

\(v^{2}-10v + 16=v^{2}-2v-8v + 16\)

Step3: Factor by grouping.

Group the first two terms and the last two terms: \((v^{2}-2v)+(-8v + 16)\)
Factor out the greatest common factor from each group: \(v(v - 2)-8(v - 2)\)

Step4: Factor out the common binomial factor.

\((v - 2)(v - 8)\)

Answer:

\((v - 2)(v - 8)\)