Question

Part A:

Factor 2x^2b^2 + xb^2 - 362:
(x + 19)(2xb^2 - 19)

Part B:
Factor x^2 + 10x + 25:
(x + 5)(x + 5) or (x + 5)^2

Part C:
Factor x^2 - 49:
(x + 7)(x - 7)

Answer 1

The quadratic formula, −b ± √(b² - 4ac) / (2a), is used to solve quadratic equations. By substituting the specific coefficients a, b, and c into the formula, two possible solutions for x are obtained.

Step-by-step explanation:

To factor quadratic equations such as x² + 0.0211x - 0.0211 = 0 or x² + 1.2 x 10-2x - 6.0 × 10-3 = 0, we can use the quadratic formula. This formula can be written as:

x = −b ± √(b² - 4ac) / (2a)

Using the given examples, we'll substitute the values of a, b, and c into the quadratic formula to solve for x. In the case of the first example with a = 1, b = 0.0211, and c = -0.0211, the calculation would be:

x = −0.0211± √(0.0211² − 4(1)(− 0.0211)) / (2(1))

After calculating the discriminant (b² - 4ac) and determining the square root, the plus/minus operation yields two possible solutions for x.