Question

1. solve for the values of x by factoring.

3x² + 19x + 20 = 0
○ x = -5; x = -\frac{4}{3}
○ x = -3; x = -5
○ x = 5; x = -\frac{3}{4}
○ x = -4; x = -\frac{5}{3}

Explanation:

Step1: Factor the quadratic equation

For the quadratic equation \( 3x^2 + 19x + 20 = 0 \), we need to find two numbers that multiply to \( 3\times20 = 60 \) and add up to \( 19 \). The numbers are \( 15 \) and \( 4 \).
Rewrite the middle term: \( 3x^2 + 15x + 4x + 20 = 0 \)
Group the terms: \( (3x^2 + 15x) + (4x + 20) = 0 \)
Factor out the common factors: \( 3x(x + 5) + 4(x + 5) = 0 \)
Factor out \( (x + 5) \): \( (3x + 4)(x + 5) = 0 \)

Step2: Solve for \( x \)

Set each factor equal to zero:

• \( x + 5 = 0 \) gives \( x = -5 \)
• \( 3x + 4 = 0 \) gives \( 3x = -4 \), so \( x = -\frac{4}{3} \)

Answer:

\( x = -5 \); \( x = -\frac{4}{3} \)