Question
Simplify the expression
x5−5x4+4x3
Evaluate
(x−1)(x−4)x3
Multiply the terms
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Evaluate
(x−1)(x−4)
Apply the distributive property
x×x−x×4−x−(−4)
Multiply the terms
x2−x×4−x−(−4)
Use the commutative property to reorder the terms
x2−4x−x−(−4)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x2−4x−x+4
Subtract the terms
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Evaluate
−4x−x
Collect like terms by calculating the sum or difference of their coefficients
(−4−1)x
Subtract the numbers
−5x
x2−5x+4
(x2−5x+4)x3
Apply the distributive property
x2×x3−5x×x3+4x3
Multiply the terms
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Evaluate
x2×x3
Use the product rule an×am=an+m to simplify the expression
x2+3
Add the numbers
x5
x5−5x×x3+4x3
Solution
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Evaluate
x×x3
Use the product rule an×am=an+m to simplify the expression
x1+3
Add the numbers
x4
x5−5x4+4x3
Show Solution

Find the roots
x1=0,x2=1,x3=4
Evaluate
(x−1)(x−4)(x3)
To find the roots of the expression,set the expression equal to 0
(x−1)(x−4)(x3)=0
Calculate
(x−1)(x−4)x3=0
Separate the equation into 3 possible cases
x−1=0x−4=0x3=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=1x−4=0x3=0
Solve the equation
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Evaluate
x−4=0
Move the constant to the right-hand side and change its sign
x=0+4
Removing 0 doesn't change the value,so remove it from the expression
x=4
x=1x=4x3=0
The only way a power can be 0 is when the base equals 0
x=1x=4x=0
Solution
x1=0,x2=1,x3=4
Show Solution
