# 6.8 Solving Equations by Factoring

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6.8 Solving Equations by Factoring
Goal: To solve equations expressed as a product of factors equal to zero and to factor and solve equations.

True or false? What value of x makes this equation true?

The Principle of Zero Products  if (a)(b) = 0, then a = 0 or b = 0
The Principle of Zero Products  if (a)(b) = 0, then a = 0 or b = 0.  if a = 0 or b = 0, then (a)(b) = 0.

the quest for “X” X

What values of “x” make this equation true? (x + 1)(x – 7) = 0

What values of “x” make this equation true? x(2x – 9) = 0

What values of “x” make this equation true? (x + 3)(x – 4) = 0

What values of “x” make this equation true? (x - 7)(x – 3) = 0

What values of “y” make this equation true? y(3y – 17) = 0

If the equation is already factored then set its factors = 0 and solve for x
If the equation is not already factored then you need to set it =0, factor it, set each of its factors =0, and solve for x

Solve for “y”: y2 + 5y = -6 Add 6 to get “0” on one side Factor
Let each factor = zero

Solve for “y”: y2 – 8y = -16 Add 16 to get “0” on one side Factor

x2 – x – 6 = 0 x = 3 or (-2)

m2 – m = 56 m = 8 or (-7)

k2 – 3k = 28 m = 7 or (-4)

“root” For a polynomial containing a variable, any value of the variable that makes the value of the polynomial = zero is called a “root” of the polynomial. Find the roots of x2 – 5x = 0

Find the roots of 25x2 – 16

Assignment Page 289 (6-20, 28-46, 56-60) even

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