Solving polynomial Equations in Factored Form

1
Solving polynomial Equations in Factored Form

• MM1A2f
• Goal solve polynomial equations
• Factor trinomials of the form x2 bx c

2
Zero Product Property

• The zero-product property is used to solve an
  equation when one side is zero and the other side
  is a product of polynomial factors
• Solutions are also called roots

3
Zero Product Property

• Solve
• (x 3)(x 6) 0
• x 3 0 or x 6 0 zero prod. Prop
• x 3 or x -6 solve

4
Zero Product Property

• Solve
• (4x 5)(4x 5) 0
• 4x5 0 or 4x 5 0 zero prod. prop
• 4x -5 or 4x 5 solve
• x -5/4 or x 5/4

5
Solve by factoring

• Solve 6x2 12x 0
• 6x (x 2) 0 factor
• 6x 0 or x 2 0 zero prod. Prop
• x 0 or x -2 solve

6
Solve by Factoring

• Solve
• -10b2 25b 0
• -5b (2b 5) 0 factor
• -5b 0 or 2b 5 0 zero prod. Prop
• b 0 or b -5/2

7
Factor trinomials x2bxc

• Use guess and check
• Use x-factor

8
Factor

• k2 6k -7
• x factor
• or guess
  and check
• (x -1)(x 7)
• x 1 0 x 7 0
• 1 1
  -7 -7
• x 1 x -7

9
Factor

• d2 5d 50
• x factor or guess
  and check
• (x 10) or (x 5 )
• x 10 0 x 5 0
• -10 -10 5 5
• x -10 x 5

10
Factor

• -2b2 14b 20
• -2(b2 7b 10) Factor out -2
• x factor or guess
  and check
• (x - 2) or (x 5 )
• x - 2 0 x 5 0
• 2 2 5 5
• x 2 x 5