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Mastering Equation Factoring: A Guide to Quadratic Equations

Learn to solve quadratic equations using factorization methods. Understand the principles of zero products & test your skills with practice problems. Perfect for students & math enthusiasts.

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Mastering Equation Factoring: A Guide to Quadratic Equations

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  1. CHAPTER 8.5 Solve equations by factoring.

  2. Principal of Zero Products • If the product of two factors is zero, then at least one of the factors must be zero. • If (a)(b)=0, then a=0 or b=0

  3. Quadratic Equations • Are equations in the form of ax2+bx+c=0, a=0. • A quadratic equation is in standard form when written in descending order and set equal to zero.

  4. Solve (x-2)(x-3)=0 • If (a)(b)=0, then a=0 or b=0 • So, either x-2=0 or x-3=0 • What number makes x-2=0 a true statement: x=2. • What number makes x-3=0 a true statement: x=3. • Or solve for x-2 = 0 x-3 = 0 • +2 +2 +3 +3 • x = 2 x = 3

  5. Solve 2x2+x=6 • Write the equation in standard form. • 2x2+x-6=0. • Factor by preferred method. • 2x2+x-6=0 • (2x-3)(x+2)= 0 • 2x-3= 0 or x+2= 0 • Solve for x +3 +3 -2 -2 • 2x=3 • x= 3 • 2 x=-2 • . • Check by substitution.

  6. Solve 2x2-50=0 • Factor GCF 2(x2-25)=0 • Continue factoring 2(x-5)(x+5)=0 • 2=0 or x-5=0 or x+5=0 • Solve for x in each case. • 2=0 x=5 or x=-5 • Solutions x = -5,5 • 2 is not a solution. • Check by substitution.

  7. Solve (x-3)(x-10)=-10 • To set up as a Quadratic Equation, FOIL the left side of equation and then add ten to both sides. x2-13x+40=0 • Factor (x-5)(x-8)=0 • Either x-5=0 or x-8=0 • Solutions are • x=8,5 • Check by substitution.

  8. Solve (x+2)(x-7)=52 • To set up as a Quadratic Equation, FOIL the left side of equation and then subtract 52 from both sides. x2-5x- 66=0 • Factor (x+6)(x-11)=0 • Either x+6=0 or x-11=0 • Solutions are • x=-6,11 • Check by substitution.

  9. NOW YOU TRY! • 1. 3x(x-4)=0 • 4,0 • 2. 16x2-4=0 • -1 , 1 • 2 2 • 3. x2-6x=7 • -1,7 • 4. (x+3)(x-5)=9 • -4, 6

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