https://file.aiquickdraw.com/mathbot/file/17266711160552rypjrfm.jpg

Let's solve each of the quadratic equations shown in the image.

### 1. First Equation: 
\[
x^2 - 4x + 3 = 0
\]
We will factor this quadratic:
\[
x^2 - 4x + 3 = (x - 3)(x - 1) = 0
\]
Thus, the solutions are:
\[
x = 3 \quad \text{or} \quad x = 1
\]

### 2. Second Equation:
\[
x^2 + 8x + 15 = 0
\]
Factoring the quadratic:
\[
x^2 + 8x + 15 = (x + 5)(x + 3) = 0
\]
So, the solutions are:
\[
x = -5 \quad \text{or} \quad x = -3
\]

### 3. Third Equation:
\[
x^2 - 11x + 10 = 0
\]
Factoring the quadratic:
\[
x^2 - 11x + 10 = (x - 10)(x - 1) = 0
\]
The solutions are:
\[
x = 10 \quad \text{or} \quad x = 1
\]

Let me know if you want a detailed explanation of any step! Also, here are some related questions to explore:

1. How do you factor quadratics with coefficients other than 1?
2. What is the quadratic formula, and how can it be applied to solve these equations?
3. Can completing the square be used for solving any of these equations?
4. What are the properties of quadratic functions in graph form?
5. How do you verify the solutions of a quadratic equation?

**Tip:** Always check your factored equation by expanding it back to ensure it matches the original equation!

Solve the quadratic equations x^2 - 4x + 3 = 0, x^2 + 8x + 15 = 0, and x^2 - 11x + 10 = 0.

This page provides a detailed step-by-step solution to solving three quadratic equations using factoring: x^2 - 4x + 3 = 0, x^2 + 8x + 15 = 0, and x^2 - 11x + 10 = 0. Ideal for students in Grades 8-10 learning algebra and quadratic equations.

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