Solving Equations by Factoring (x+3)(2x-1) (3x-1)(x-2)

Don't worry about moving slowly, worry about standing still. -- Chinese proverb

Solidify factoring in terms of solving equations.

If a = 0 or b = 0 then ab = 0 You can use this property to solve certain equations!

(x+2)(x-5) =0 Since the answer is zero, you know that one of the factors has got to equal zero. Set each equal to zero x+2=0x-5=0 x=-2x=5 Therefore the solution set is {-2,5}, x is either equal to -2 or 5.

5n(n-3)(n-4)=0 Again, you know one of the factors must equal zero so set them all to zero. 5n =0n-3= 0n-4=0 n=0n=3n=4 The solution set is {0, 3, 4}

Polynomial Equation- an equation whose sides are both polynomials Linear equation-> ax+b=0 Quadratic equation-> ax² + bx +c Cubic equation-> ax³ + bx² + cx + d

2x² + 5x = Transform into standard form 1. 2x² +5x -12 = 0 2. Factor the left side 1. (2x-3)(x+4)=0 3. Set each factor equal to zero and solve. 1. 2x-3 = 0x+4 = 0 2. x=3/2x=-4 4. Check your solutions

18y³ +8y +24y²=0 1. Transform into standard form 1. 18y³ + 24y² + 8y= 0 2. Factor completely 1. 2y(9y²+ 12y+4) 2. 2y(3y+2)² 3. Set each part equal to zero 1. 2y=0; y=0 2. (3y+2)²; y=-2/3 4. CHECK!

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