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The image you uploaded contains two quadratic expressions to factor:

1. \( x^2 + 23x - 50 \)
2. \( 20x^2 + 17x + 3 \)

### Let's factor these one by one:

#### 1. \( x^2 + 23x - 50 \)

To factor this quadratic expression, we need to find two numbers that multiply to \(-50\) (the constant term) and add to \(23\) (the coefficient of \(x\)).

The pair of numbers that satisfies these conditions are \(25\) and \(-2\):

\[
x^2 + 23x - 50 = (x + 25)(x - 2)
\]

So, the factored form is:

\[
(x + 25)(x - 2)
\]

#### 2. \( 20x^2 + 17x + 3 \)

For this quadratic expression, we can use the method of factoring by grouping:

First, find two numbers that multiply to \(20 \times 3 = 60\) (the product of the leading coefficient and the constant term) and add to \(17\) (the middle coefficient). The pair of numbers that work here are \(15\) and \(2\).

So, rewrite the middle term \(17x\) as \(15x + 2x\):

\[
20x^2 + 15x + 2x + 3
\]

Next, group the terms:

\[
(20x^2 + 15x) + (2x + 3)
\]

Factor out the greatest common factors from each group:

\[
5x(4x + 3) + 1(2x + 3)
\]

Notice that we made a mistake in factoring. The correct grouping should have been:

\[
(20x^2 + 15x) + (2x + 3) = 5x(4x + 3) + 1(4x + 3)
\]

Thus, the correct factorization is:

\[
(5x + 1)(4x + 3)
\]

### Final Answers:
1. \( x^2 + 23x - 50 = (x + 25)(x - 2) \)
2. \( 20x^2 + 17x + 3 = (5x + 1)(4x + 3) \)

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Would you like further details on how these factorizations were performed or have any other questions?

### Relative Questions:
1. How do you factor trinomials when the leading coefficient is greater than 1?
2. What are the steps to check if a quadratic expression can be factored using integer pairs?
3. How do you solve quadratic equations using the factored form?
4. What is the quadratic formula, and when is it used instead of factoring?
5. How can factoring be applied to solve real-world problems?

### Tip:
Always double-check your factor pairs to ensure they multiply and add up correctly to the original quadratic coefficients.

Factor the quadratic expressions x^2 + 23x - 50 and 20x^2 + 17x + 3.

Learn how to factor the quadratic expressions x^2 + 23x - 50 and 20x^2 + 17x + 3. This guide provides step-by-step solutions and explanations on factoring by grouping and finding the correct factor pairs. Suitable for students in Grades 9-10.

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