Question

what are the factors of $m^2 - 12m + 20$?
$\bigcirc$ $m - 14$ and $m - 6$
$\bigcirc$ $m - 10$ and $m - 2$
$\bigcirc$ $m - 9$ and $m - 3$
$\bigcirc$ $m - 5$ and $m - 4$

Explanation:

Step1: Recall factoring quadratic

We need two numbers that multiply to \(20\) and add to \(-12\) (since the middle term is \(-12m\) and the constant term is \(+20\)).

Step2: Find the numbers

Let the numbers be \(a\) and \(b\) such that \(a\times b = 20\) and \(a + b=- 12\). The numbers are \(-10\) and \(-2\) because \((-10)\times(-2)=20\) and \(-10+( - 2)=-12\).

Step3: Factor the quadratic

Using the numbers, we can factor \(m^{2}-12m + 20=(m - 10)(m - 2)\)

Answer:

\(m - 10\) and \(m - 2\) (the second option: \(m - 10\) and \(m - 2\))