Polynomial and Radical Equations -- Section 1.6 --
 Solve for x:  20x3 – 125x = 0
 Solve Step Check 20x3 – 125x = 0 5x(4x2 – 25) = 0 5x(2x – 5)(2x + 5) = 0 5x = 0 or 2x – 5 = 0 or  2x + 5 = 0 x = 0 , x = 5/2 or x = -5/2 Try factoring.  It usually is the easiest method. LCM = 5x Keeping factoring.  Perfect Square TrinomialSet each factor to zeroClick Solving Linear Equations for help If x  = 0, then 20(0)3 – 125(0) = 0     0  – 0 = 0 If x  = 5/2, then 20(5/2)3 – 125(5/2) = 0     20(125/8)  – 125(5/2) = 0 625/2  – 625/2 = 0    0 = 0 If x  = -5/2, then 20(-5/2)3 – 125(-5/2) = 0     20(-125/8)  – 125(-5/2) = 0 -625/2  + 625/2 = 0      0 = 0 Solve for x:     36x3 – 64x = 0 [Solution]
 Solve for x:  2x3 + x2  – 2x – 1 = 0
 Solve Step Check 2x3 + x2  – 2x – 1 = 0 Use the grouping method If x  = -½, then 2(-½)3+(-½)2–2(-½)–1=0     2(-1/8)+¼+1–1 = 0 -¼ + ¼ = 0 0 = 0 If x  = 1, then 2(1)3+(1)2–2(1)–1 = 0     2 + 1 – 2 –1 = 0 0 = 0 If x  = -1, then 2(-1)3+(-1)2–2(-1)–1 = 0     -2 + 1 + 2 –1 = 0 0 = 0 x2 (2x + 1)  – 2x – 1 = 0 Look for a pattern.  Factor a x2 form the first 2 terms. x2 (2x + 1)  – 1(2x + 1) = 0 I see a 2x + 1 pattern.  Factor out a -1 from the last 2 terms. (2x + 1)(x2  – 1) = 0 Now factor out a (2x + 1) from each part. (2x + 1)(x – 1)(x + 1) = 0 Finish factoring!  Difference of two squares. 2x + 1 = 0 or x – 1 or  x + 1 = 0 Set each factor to zero x = -1/2 , x = 1 or x = -1 Click Solving Linear Equations for help. Use grouping to solve a cubic equation with 4 terms.  If this doesn't work then we are stuck for now.  Try it with 4th degree equations too. Solve for x:  x3 + 3x2  – 4x – 12 = 0 [Solution]
 Solve for x:
 Solve Step Check Add 3 to both sides. If x  = -4, then Square both sides to undo the square root. 1 – 2x = 9 Solve for x. -2x = 8 Click Solving Linear Equations for help. x = -4 Done!! Note: Solve for x: [Solution]
 Solve for x:
 Solve Step Check Add 5 to both sides. If x  = -1, then If x  = -23/9, then Square both sides to undo the square root. 9x2 + 30x + 25 = 2 –  2x Remember to use FOIL 9x2 + 30x + 25 = 2 –  2x Set equal to 0. Add  2x Subtract 2 9x2 + 32x + 23 = 0 (x + 1)(9x + 23) = 0 It factors! x + 1 = 0 or 9x + 23 = 0 Set each factor to zero x = -1 or x = -23/9 Click Solving Linear Equations for help. x = -1 is the only solution Done!! Always check the answers to make sure they work.  They may not work.
 Solve for x:
 [Solution]

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