1 MATH 1310 Section 2.5

2 Other Techniques for Solving EquationsSolving by Factoring: Factoring can be used to solve many types of equations. Always begin by Factoring Completely. Then, set each factor equal to zero.

3 Find all the solutions of x3 = x

4 Find all solutions to x3 + 3x2 + 2x + 6 = 0

5 Equations involving radicals: If an equation involves a square root (also called a radical), you must isolate the radical, square both sides, and solve the remaining equation. Be certain to check your answers!

6 Find all solutions to 𝑥+8 −2=𝑥

7 Find all solutions to 𝑥+8 −2=𝑥

8 Extraneous Solutions: In a radical solution, you may “create” additional answers that are not correct. These must be rejected!

9 Find all solutions to 3𝑥+1 −1=𝑥

10 Solving by Substitution:When a function looks, “almost” quadratic, you may want to solve it by relating it to another function. x10 – x5 – 6 = 0 If the exponents go “full amount  half amount  nothing” then you can rewrite as a quadratic. Let u = x5, then x10 – x5 – 6 = 0  u2 – u – 6 = 0

11 x1/2 + 2x1/4 – 15 = 0

12 Popper # 1 Solve the following: x3 = 9xa. 0, 3 b. 0, 9, -9 c. 0,-3, 3 d. -3, 3 2. Solve the following: 𝑥+ 𝑥+1 =5 a. 8, 3 b. 3 c. 8 d. No Answer 3. Solve the following: 8 𝑥 𝑥 =3 a. 3 b. -1/3 c. -1 d. 3, -1/3

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