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The image has been opened successfully. It shows four quadratic equations that need to be factorized. Let's work through each one:

### a. \( x^2 - 5x + 6 \)
We need to factor this quadratic:
\[
x^2 - 5x + 6 = (x - ?)(x - ?)
\]
Find two numbers that multiply to \(6\) and add to \(-5\). These numbers are \(-2\) and \(-3\). Thus:
\[
x^2 - 5x + 6 = (x - 2)(x - 3)
\]

### b. \( x^2 - 3x + 2 \)
Factor:
\[
x^2 - 3x + 2 = (x - ?)(x - ?)
\]
The numbers that multiply to \(2\) and add to \(-3\) are \(-1\) and \(-2\). Hence:
\[
x^2 - 3x + 2 = (x - 1)(x - 2)
\]

### c. \( x^2 - x - 2 \)
Factor:
\[
x^2 - x - 2 = (x + ?)(x - ?)
\]
Here, the numbers that multiply to \(-2\) and add to \(-1\) are \(1\) and \(-2\). Therefore:
\[
x^2 - x - 2 = (x + 1)(x - 2)
\]

### d. \( x^2 + 4x + 3 \)
Factor:
\[
x^2 + 4x + 3 = (x + ?)(x + ?)
\]
The numbers that multiply to \(3\) and add to \(4\) are \(1\) and \(3\). So:
\[
x^2 + 4x + 3 = (x + 1)(x + 3)
\]

Would you like more details or have any further questions? Here are some related questions:

1. How do you determine the factors of a quadratic equation?
2. What is the process for factoring quadratics of the form \( ax^2 + bx + c \) where \( a \neq 1 \)?
3. How would you verify that your factorization is correct?
4. Can all quadratic equations be factorized this way?
5. What happens if the quadratic does not have real roots?

**Tip:** When factoring quadratic equations, always look for pairs of numbers that multiply to the constant term and add to the coefficient of the linear term.

Factoriser : a. x^2 - 5x + 6 = (x - ?)(x - ?), b. x^2 - 3x + 2 = (x - ?)(x - ?), c. x^2 - x - 2 = (x + ?)(x - ?), d. x^2 + 4x + 3 = (x + ?)(x + ?)

Learn how to factor quadratic equations such as x^2 - 5x + 6 with step-by-step explanations. This exercise covers essential algebraic techniques in quadratic factorization and is ideal for students in grades 8-10.

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