[tex]\large\sf\underline{ANSWER:}[/tex]
1. x = 0 or x = 1 or x = -5
x( x - 1 )( x + 5 ) = 0
Apply Zero Product Property
x = 0 or x - 1 = 0 or x + 5 = 0
Rearrange unknown terms to the left side of the equation
x = 1
2. x = 0 or x = -3 or x = -4
x³ + 7x² + 12x = 0
Factor out
x( x² + 7x + 12 ) = 0
Factor the expression
x( x + 3 )( x + 4 ) = 0
3. x = 1 or x = -2
x³ + 3x² - 4 = 0
Factor the cubic expression
( x - 1 )( x + 2 )² = 0
Use the Rational Root Theorem to identify a root of the equation
x - 1 = 0 or x + 2 = 0
4. x = 6 or x = -7 or x = -8
x³ + 9x² - 34x - 336 = 0
Factor the cubic expression
( x - 6 )( x + 7 )( x + 8 ) = 0
Use the Rational Root Theorem to identify a root of the equation
x - 6 = 0 or x + 7 = 0 or x + 8 = 0
5. x = 3 or x = 4 + √11 or x = 4 - √11
x³ - 11x² + 29x - 15 = 0
Factor the cubic expression
( x - 3 )( x² - 8x + 5 ) = 0
Use the Rational Root Theorem to identify a root of the equation
x - 3 = 0 or x² - 8x + 5 = 0
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