Question

1. solve for the values of x by factoring.

7x² - 26x - 8 = 0
○ x = -2; x = 4/7
○ x = 2; x = -4/7
○ x = 4; x = -2/7
○ x = -4; x = 2/7

Explanation:

Step1: Factor the quadratic equation

For the quadratic equation \( 7x^2 - 26x - 8 = 0 \), we need to find two numbers that multiply to \( 7\times(-8)=-56 \) and add up to \( -26 \). The numbers are \( -28 \) and \( 2 \).
Rewrite the middle term: \( 7x^2 - 28x + 2x - 8 = 0 \)
Group the terms: \( (7x^2 - 28x) + (2x - 8) = 0 \)
Factor out the common factors: \( 7x(x - 4) + 2(x - 4) = 0 \)
Factor out \( (x - 4) \): \( (7x + 2)(x - 4) = 0 \)

Step2: Solve for \( x \)

Set each factor equal to zero:

• \( 7x + 2 = 0 \) gives \( 7x = -2 \), so \( x = -\frac{2}{7} \)
• \( x - 4 = 0 \) gives \( x = 4 \)

Answer:

\( x = 4; x = -\frac{2}{7} \)