Factoring to Solve Polynomial Equations

Factor:

p² - 14p

• p(1 - 14)

• 2p(p - 7)

• p²(1-14)

• p(p - 14)

Factor by Grouping:
x³ - 5x² + 5x - 25

• (x² - 5) (x - 5)
• (x² + 5) (x - 5)
• (x² + 5) (x + 5)
• (x² - 1) (x - 25)

Factor Completely:  3n² - 15n + 18

• (n - 2)(n - 3)
• 3(n + 2)(n + 3)
• (3n - 9)(n - 2)
• 3(n - 3)(n - 2)

• Factor

• Subtract 6 from both sides to set the equation equal to 0

• Set each factor equal to 0

• Combine like terms

What are the 2 characteristics we look for when trying to solve a quadratic equation?

• Factor and cancel

• Distribute and combine like terms

• There is no such thing as a quadratic equation

What should you do first in solving this equation?
x² + 6x - 13 = 3

• Get factored form
• Find two numbers which add to make 6 and multiply to make -13
• Make it equal 0 by subtracting 3 on each side
• Type it all in a calculator.

Convert x² - 9x + 20 = 0 to factored form and solve.

• (x-10)(x+2); x = -2, 10

• (x+4)(x+5); x = -5, -4

• (x-4)(x-5); x = 4, 5

• Not factorable

Factor: 49x² - 100

• (49x + 100)(x - 1)
• (7x - 10)(7x + 10)
• (49x - 10)(x + 10)
• (7x -10)(7x - 10)

Factor x² + 6x + 9 = 0 and solve for x.

• (x+3)(x+3); x = -3

• (x+4)(x+5); x=-4, -5

• (x-3)(x-3); x=3

• Not factorable

Factor 6x²-27x

• (6x+1)(x+3)
• 3x(2x-9)
• 6x(x-9)
• (3x-9)(2x+3)