Question

which shows the factored form of $x^2 - 12x - 45$?
○ $(x + 3)(x - 15)$
○ $(x - 3)(x - 15)$
○ $(x + 3)(x + 15)$
○ $(x - 3)(x + 15)$

Explanation:

Step1: Recall factoring trinomials

To factor \(x^2 - 12x - 45\), we need two numbers that multiply to \(-45\) and add up to \(-12\).

Step2: Find the numbers

Let the numbers be \(a\) and \(b\) such that \(a\times b=-45\) and \(a + b=-12\). The numbers are \(3\) and \(-15\) because \(3\times(-15)=-45\) and \(3+(-15)=-12\).

Step3: Write the factored form

Using these numbers, the factored form of \(x^2 - 12x - 45\) is \((x + 3)(x - 15)\) (since \(x^2+bx + c=(x + m)(x + n)\) where \(m\) and \(n\) are the numbers we found). We can verify by multiplying \((x + 3)(x - 15)=x^2-15x + 3x-45=x^2-12x - 45\).

Answer:

A. \((x + 3)(x - 15)\)