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To factor the quadratic expression \( x^2 + 19x + 20 \), we need to find two numbers that multiply to \( 20 \) and add up to \( 19 \).

1. List pairs of factors of \( 20 \): 
   - \( 1 \times 20 = 20 \)
   - \( 2 \times 10 = 20 \)
   - \( 4 \times 5 = 20 \)

2. Check which pair adds up to \( 19 \):
   - The pair \( 1 \) and \( 20 \) adds up to \( 19 \).

3. Rewrite the expression as:
   \[
   x^2 + 19x + 20 = (x + 1)(x + 20)
   \]

Thus, the completely factored form is:
\[
(x + 1)(x + 20)
\]

Would you like more details or have any questions?

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### Related Questions

1. How would you factor a quadratic expression with a negative middle term?
2. How can we verify that our factored expression is correct?
3. What if the constant term was negative—how would the factors change?
4. How do you factor when there is a leading coefficient other than 1?
5. How can factoring be applied to solve quadratic equations?

**Tip:** Always double-check by expanding your factors to see if you return to the original expression.

Learn how to factor the quadratic expression x^2 + 19x + 20. This detailed solution explains the steps to find factors that multiply to 20 and add up to 19. Ideal for students in Grades 8-10.

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