Question
13 Simplify the polynomial. Answer m \( \begin{array}{l}(x-4)(x+6)\end{array} \)
Ask by Wang Rodriquez. in the United States
Mar 09,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The simplified polynomial is \( x^2 + 2x - 24 \).
Solution
1. Expand the product using the distributive property (FOIL method):
- First: \( x \cdot x = x^2 \)
- Outer: \( x \cdot 6 = 6x \)
- Inner: \( -4 \cdot x = -4x \)
- Last: \( -4 \cdot 6 = -24 \)
2. Combine like terms:
\[
6x - 4x = 2x
\]
3. The simplified form of the polynomial is:
\[
x^2 + 2x - 24
\]
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Simplify this solution Bonus Knowledge
To simplify the polynomial \( (x-4)(x+6) \), you can apply the distributive property, commonly known as the FOIL method (First, Outer, Inner, Last). When you multiply, you'll get: 1. First: \( x \cdot x = x^2 \) 2. Outer: \( x \cdot 6 = 6x \) 3. Inner: \( -4 \cdot x = -4x \) 4. Last: \( -4 \cdot 6 = -24 \) Now combine like terms \( (6x - 4x) \) to have: \( x^2 + 2x - 24 \) So, the simplified polynomial is \( x^2 + 2x - 24 \). Want to visualize it? Think of it like opening a gift, layer by layer revealing the surprise inside, which in this case is your beautifully simplified polynomial!
