Question
Simplify the expression
x4−13x3+53x2−83x+42
Evaluate
(x−1)(x−2)(x−3)(x−7)
Multiply the terms
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Evaluate
(x−1)(x−2)
Apply the distributive property
x×x−x×2−x−(−2)
Multiply the terms
x2−x×2−x−(−2)
Use the commutative property to reorder the terms
x2−2x−x−(−2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x2−2x−x+2
Subtract the terms
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Evaluate
−2x−x
Collect like terms by calculating the sum or difference of their coefficients
(−2−1)x
Subtract the numbers
−3x
x2−3x+2
(x2−3x+2)(x−3)(x−7)
Multiply the terms
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Evaluate
(x2−3x+2)(x−3)
Apply the distributive property
x2×x−x2×3−3x×x−(−3x×3)+2x−2×3
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−x2×3−3x×x−(−3x×3)+2x−2×3
Use the commutative property to reorder the terms
x3−3x2−3x×x−(−3x×3)+2x−2×3
Multiply the terms
x3−3x2−3x2−(−3x×3)+2x−2×3
Multiply the numbers
x3−3x2−3x2−(−9x)+2x−2×3
Multiply the numbers
x3−3x2−3x2−(−9x)+2x−6
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x3−3x2−3x2+9x+2x−6
Subtract the terms
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Evaluate
−3x2−3x2
Collect like terms by calculating the sum or difference of their coefficients
(−3−3)x2
Subtract the numbers
−6x2
x3−6x2+9x+2x−6
Add the terms
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Evaluate
9x+2x
Collect like terms by calculating the sum or difference of their coefficients
(9+2)x
Add the numbers
11x
x3−6x2+11x−6
(x3−6x2+11x−6)(x−7)
Apply the distributive property
x3×x−x3×7−6x2×x−(−6x2×7)+11x×x−11x×7−6x−(−6×7)
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−x3×7−6x2×x−(−6x2×7)+11x×x−11x×7−6x−(−6×7)
Use the commutative property to reorder the terms
x4−7x3−6x2×x−(−6x2×7)+11x×x−11x×7−6x−(−6×7)
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
x4−7x3−6x3−(−6x2×7)+11x×x−11x×7−6x−(−6×7)
Multiply the numbers
x4−7x3−6x3−(−42x2)+11x×x−11x×7−6x−(−6×7)
Multiply the terms
x4−7x3−6x3−(−42x2)+11x2−11x×7−6x−(−6×7)
Multiply the numbers
x4−7x3−6x3−(−42x2)+11x2−77x−6x−(−6×7)
Multiply the numbers
x4−7x3−6x3−(−42x2)+11x2−77x−6x−(−42)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x4−7x3−6x3+42x2+11x2−77x−6x+42
Subtract the terms
More Steps

Evaluate
−7x3−6x3
Collect like terms by calculating the sum or difference of their coefficients
(−7−6)x3
Subtract the numbers
−13x3
x4−13x3+42x2+11x2−77x−6x+42
Add the terms
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Evaluate
42x2+11x2
Collect like terms by calculating the sum or difference of their coefficients
(42+11)x2
Add the numbers
53x2
x4−13x3+53x2−77x−6x+42
Solution
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Evaluate
−77x−6x
Collect like terms by calculating the sum or difference of their coefficients
(−77−6)x
Subtract the numbers
−83x
x4−13x3+53x2−83x+42
Show Solution

Find the roots
x1=1,x2=2,x3=3,x4=7
Evaluate
(x−1)(x−2)(x−3)(x−7)
To find the roots of the expression,set the expression equal to 0
(x−1)(x−2)(x−3)(x−7)=0
Separate the equation into 4 possible cases
x−1=0x−2=0x−3=0x−7=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−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=1x=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=1x=2x=3x−7=0
Solve the equation
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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=1x=2x=3x=7
Solution
x1=1,x2=2,x3=3,x4=7
Show Solution
