Question
Simplify the expression
x4−4x3+3x2
Evaluate
(x−1)x2(x−3)
Multiply the first two terms
x2(x−1)(x−3)
Multiply the terms
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Evaluate
x2(x−1)
Apply the distributive property
x2×x−x2×1
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−x2×1
Any expression multiplied by 1 remains the same
x3−x2
(x3−x2)(x−3)
Apply the distributive property
x3×x−x3×3−x2×x−(−x2×3)
Multiply the terms
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Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
x4−x3×3−x2×x−(−x2×3)
Use the commutative property to reorder the terms
x4−3x3−x2×x−(−x2×3)
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
x4−3x3−x3−(−x2×3)
Use the commutative property to reorder the terms
x4−3x3−x3−(−3x2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x4−3x3−x3+3x2
Solution
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Evaluate
−3x3−x3
Collect like terms by calculating the sum or difference of their coefficients
(−3−1)x3
Subtract the numbers
−4x3
x4−4x3+3x2
Show Solution

Find the roots
x1=0,x2=1,x3=3
Evaluate
(x−1)(x2)(x−3)
To find the roots of the expression,set the expression equal to 0
(x−1)(x2)(x−3)=0
Calculate
(x−1)x2(x−3)=0
Multiply the first two terms
x2(x−1)(x−3)=0
Separate the equation into 3 possible cases
x2=0x−1=0x−3=0
The only way a power can be 0 is when the base equals 0
x=0x−1=0x−3=0
Solve the equation
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Evaluate
x−1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
x=0x=1x−3=0
Solve the equation
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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=0x=1x=3
Solution
x1=0,x2=1,x3=3
Show Solution
