Welcome math enthusiasts! Below you'll find the solutions to our latest set of mind-boggling algebra exercises. Let's dive in and unravel the mysteries of numbers!
Given: \( ax^2 + bx + c = 0 \)
Solution: Use the quadratic formula \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \).
Example: For \( 2x^2 - 4x - 6 = 0 \), \( a = 2, b = -4, c = -6 \).
Solution: \( x = \frac{4 \pm \sqrt{(-4)^2 - 4 \cdot 2 \cdot (-6)}}{4} = \frac{4 \pm \sqrt{64}}{4} = 3 \, \text{or} \, -1 \).
Problem: Factor the polynomial \( x^3 - 3x^2 + 3x - 1 \).
Solution: Use synthetic division and factorization techniques. Result is \( (x - 1)^3 \).
For more exercises and solutions, visit our Algebra Resources or explore our Other Topics.