Question
Simplify the expression
x4−12x3+41x2−42x
Evaluate
x(x−2)(x−3)(x−7)
Multiply the terms
More Steps

Evaluate
x(x−2)
Apply the distributive property
x×x−x×2
Multiply the terms
x2−x×2
Use the commutative property to reorder the terms
x2−2x
(x2−2x)(x−3)(x−7)
Multiply the terms
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Evaluate
(x2−2x)(x−3)
Apply the distributive property
x2×x−x2×3−2x×x−(−2x×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
x3−x2×3−2x×x−(−2x×3)
Use the commutative property to reorder the terms
x3−3x2−2x×x−(−2x×3)
Multiply the terms
x3−3x2−2x2−(−2x×3)
Multiply the numbers
x3−3x2−2x2−(−6x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x3−3x2−2x2+6x
Subtract the terms
More Steps

Evaluate
−3x2−2x2
Collect like terms by calculating the sum or difference of their coefficients
(−3−2)x2
Subtract the numbers
−5x2
x3−5x2+6x
(x3−5x2+6x)(x−7)
Apply the distributive property
x3×x−x3×7−5x2×x−(−5x2×7)+6x×x−6x×7
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−x3×7−5x2×x−(−5x2×7)+6x×x−6x×7
Use the commutative property to reorder the terms
x4−7x3−5x2×x−(−5x2×7)+6x×x−6x×7
Multiply the terms
More Steps

Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
x4−7x3−5x3−(−5x2×7)+6x×x−6x×7
Multiply the numbers
x4−7x3−5x3−(−35x2)+6x×x−6x×7
Multiply the terms
x4−7x3−5x3−(−35x2)+6x2−6x×7
Multiply the numbers
x4−7x3−5x3−(−35x2)+6x2−42x
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x4−7x3−5x3+35x2+6x2−42x
Subtract the terms
More Steps

Evaluate
−7x3−5x3
Collect like terms by calculating the sum or difference of their coefficients
(−7−5)x3
Subtract the numbers
−12x3
x4−12x3+35x2+6x2−42x
Solution
More Steps

Evaluate
35x2+6x2
Collect like terms by calculating the sum or difference of their coefficients
(35+6)x2
Add the numbers
41x2
x4−12x3+41x2−42x
Show Solution

Find the roots
x1=0,x2=2,x3=3,x4=7
Evaluate
x(x−2)(x−3)(x−7)
To find the roots of the expression,set the expression equal to 0
x(x−2)(x−3)(x−7)=0
Separate the equation into 4 possible cases
x=0x−2=0x−3=0x−7=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=0x=2x−3=0x−7=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=2x=3x−7=0
Solve the equation
More Steps

Evaluate
x−7=0
Move the constant to the right-hand side and change its sign
x=0+7
Removing 0 doesn't change the value,so remove it from the expression
x=7
x=0x=2x=3x=7
Solution
x1=0,x2=2,x3=3,x4=7
Show Solution
