I found a list of questions in the document. Let me start by answering the first one.

### Question 1

#### (a) Expand and simplify \((x – 2)(2x + 3)(x + 1)\)

First, we will expand the first two terms \((x - 2)(2x + 3)\):

\[ (x - 2)(2x + 3) = x(2x + 3) - 2(2x + 3) \]
\[ = 2x^2 + 3x - 4x - 6 \]
\[ = 2x^2 - x - 6 \]

Next, we multiply this result by \((x + 1)\):

\[ (2x^2 - x - 6)(x + 1) = 2x^2(x + 1) - x(x + 1) - 6(x + 1) \]
\[ = 2x^3 + 2x^2 - x^2 - x - 6x - 6 \]
\[ = 2x^3 + x^2 - 7x - 6 \]

So, the expanded and simplified form is:

\[ 2x^3 + x^2 - 7x - 6 \]

#### (b) Find the value of \(n\).

Without further context or additional information, it is unclear which specific \(n\) is being referred to. Please provide more details or the complete problem statement for accurate assistance.

#### (c) Solve \(5x^2 - 4x - 3 = 0\)

We will solve the quadratic equation using the quadratic formula:

\[ x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \]

For the equation \(5x^2 - 4x - 3 = 0\):
- \(a = 5\)
- \(b = -4\)
- \(c = -3\)

First, calculate the discriminant:

\[ \Delta = b^2 - 4ac = (-4)^2 - 4(5)(-3) \]
\[ = 16 + 60 \]
\[ = 76 \]

Now, find the solutions:

\[ x = \frac{-(-4) \pm \sqrt{76}}{2(5)} \]
\[ = \frac{4 \pm \sqrt{76}}{10} \]
\[ = \frac{4 \pm 2\sqrt{19}}{10} \]
\[ = \frac{2 \pm \sqrt{19}}{5} \]

So, the solutions to the equation \(5x^2 - 4x - 3 = 0\) are:

\[ x = \frac{2 + \sqrt{19}}{5} \quad \text{and} \quad x = \frac{2 - \sqrt{19}}{5} \]

If you need further details or have other questions, let me know!

Here are five more questions you can ask:

1. Can you solve another specific problem from the document?
2. How do you derive a specific formula used in one of the questions?
3. Can you explain a particular mathematical concept mentioned in the PDF?
4. What are the key points discussed in a certain section of the document?
5. How do you approach solving a complex equation from the file?

Tip: When working with quadratic equations, always check if they can be factored easily before using the quadratic formula. This can save time and simplify the solving process.

Learn how to expand and simplify polynomials, solve quadratic equations, and understand the quadratic formula with step-by-step solutions. This problem involves expanding and simplifying polynomials, solving a quadratic equation, and using the quadratic formula. Suitable for high school students.

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