Question

1. which expression is equivalent to $x^2 + 10x + 24$?

options:

• $(x + 3)(x + 8)$
• $(x + 4)(x + 6)$
• $(x + 2)(x + 12)$
• $(x + 1)(x + 24)$

clear all

Explanation:

Step1: Recall factoring quadratic

We need to factor \(x^2 + 10x + 24\). We look for two numbers that multiply to \(24\) and add to \(10\).

Step2: Find the numbers

The numbers \(4\) and \(6\) multiply to \(24\) (\(4\times6 = 24\)) and add to \(10\) (\(4 + 6=10\)).

Step3: Write the factored form

So, \(x^2 + 10x + 24=(x + 4)(x + 6)\). We can verify by expanding \((x + 4)(x + 6)\):
\[

$$\begin{align*} (x + 4)(x + 6)&=x\times x+x\times6 + 4\times x+4\times6\\ &=x^2+6x + 4x+24\\ &=x^2 + 10x+24 \end{align*}$$

\]

Answer:

B. \((x + 4)(x + 6)\) (assuming the second option is labeled B, if the options are labeled as A, B, C, D with A being \((x + 3)(x + 8)\), B being \((x + 4)(x + 6)\), C being \((x + 2)(x + 12)\), D being \((x + 1)(x + 24)\))