Question
Simplify the expression
x3−3x2−4x+12
Evaluate
(x2−x−6)(x−2)
Apply the distributive property
x2×x−x2×2−x×x−(−x×2)−6x−(−6×2)
Multiply the terms
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Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x3−x2×2−x×x−(−x×2)−6x−(−6×2)
Use the commutative property to reorder the terms
x3−2x2−x×x−(−x×2)−6x−(−6×2)
Multiply the terms
x3−2x2−x2−(−x×2)−6x−(−6×2)
Use the commutative property to reorder the terms
x3−2x2−x2−(−2x)−6x−(−6×2)
Multiply the numbers
x3−2x2−x2−(−2x)−6x−(−12)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x3−2x2−x2+2x−6x+12
Subtract the terms
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Evaluate
−2x2−x2
Collect like terms by calculating the sum or difference of their coefficients
(−2−1)x2
Subtract the numbers
−3x2
x3−3x2+2x−6x+12
Solution
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Evaluate
2x−6x
Collect like terms by calculating the sum or difference of their coefficients
(2−6)x
Subtract the numbers
−4x
x3−3x2−4x+12
Show Solution

Factor the expression
(x−3)(x+2)(x−2)
Evaluate
(x2−x−6)(x−2)
Solution
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Evaluate
x2−x−6
Rewrite the expression
x2+(2−3)x−6
Calculate
x2+2x−3x−6
Rewrite the expression
x×x+x×2−3x−3×2
Factor out x from the expression
x(x+2)−3x−3×2
Factor out −3 from the expression
x(x+2)−3(x+2)
Factor out x+2 from the expression
(x−3)(x+2)
(x−3)(x+2)(x−2)
Show Solution

Find the roots
x1=−2,x2=2,x3=3
Evaluate
(x2−x−6)(x−2)
To find the roots of the expression,set the expression equal to 0
(x2−x−6)(x−2)=0
Separate the equation into 2 possible cases
x2−x−6=0x−2=0
Solve the equation
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Evaluate
x2−x−6=0
Factor the expression
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Evaluate
x2−x−6
Rewrite the expression
x2+(2−3)x−6
Calculate
x2+2x−3x−6
Rewrite the expression
x×x+x×2−3x−3×2
Factor out x from the expression
x(x+2)−3x−3×2
Factor out −3 from the expression
x(x+2)−3(x+2)
Factor out x+2 from the expression
(x−3)(x+2)
(x−3)(x+2)=0
When the product of factors equals 0,at least one factor is 0
x−3=0x+2=0
Solve the equation for x
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Evaluate
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=3x+2=0
Solve the equation for x
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Evaluate
x+2=0
Move the constant to the right-hand side and change its sign
x=0−2
Removing 0 doesn't change the value,so remove it from the expression
x=−2
x=3x=−2
x=3x=−2x−2=0
Solve the equation
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Evaluate
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=3x=−2x=2
Solution
x1=−2,x2=2,x3=3
Show Solution
