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Extra resources for Algebra II Essentials For Dummies (For Dummies (Math & Science))
Write the quadratic as the product of two binomials, if the quadratic is the difference of perfect squares. Taking out a greatest common factor The greatest common factor (GCF) of two or more terms is the largest number (and variable combination) that divides each of the terms evenly. Solve the equation 4x2 + 8x = 0 using factorization and the MPZ. Factor out the GCF: 4x(x + 2) = 0. Using the MPZ, you can now make one of three statements about this equation: ✓ 4 = 0, which is false — this isn’t a solution ✓x=0 ✓ x + 2 = 0, which means that x = –2 26 Algebra II Essentials For Dummies You find two solutions for the original equation 4x2 + 8x = 0: x = 0 or x = –2.
You can write the solution in interval notation as [–2, 3]. 22 Algebra II Essentials For Dummies Solve for x. Rewrite the absolute value inequality as two separate inequalities: 7 – 2x > 11 and 7 – 2x < –11. When solving the two inequalities, be sure to remember to switch the sign when you divide by –2: The solution x < –2 or x > 9, in interval notation, is (–∞, –2) or (9, ∞). Don’t write the solution x < –2 or x > 9 as 9 < x < –2. If you do, you indicate that some numbers can be bigger than 9 and smaller than –2 at the same time, which just isn’t so.
First, add 6 to both sides of the equation to get the radical by itself on the left. Then square both sides of the equation. Now set the quadratic equation equal to 0 and solve it: The two solutions work for the quadratic equation that was created, but they don’t necessarily work in the original equation. Check the work! When x = –3, you get The solution x = –3 works. Checking x = –5, you get This solution works, too. Chapter 4: Rolling Along with Rational and Radical Equations 41 Both solutions working out is more the exception rather than the rule.