Question

the model represents $x^2 - 9x + 14$. which is a factor of $x^2 - 9x + 14$? options: $x - 9$, $x - 2$, $x + 5$, $x + 7$

Explanation:

Step1: Factor the quadratic expression

To factor \(x^2 - 9x + 14\), we need two numbers that multiply to \(14\) and add up to \(-9\). The numbers are \(-2\) and \(-7\) because \((-2)\times(-7) = 14\) and \(-2 + (-7)=-9\).
So, \(x^2 - 9x + 14=(x - 2)(x - 7)\).

Step2: Identify the factor

From the factored form \((x - 2)(x - 7)\), we can see that \(x - 2\) is a factor.

Answer:

\(x - 2\) (corresponding to the option: \(x - 2\))