Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x5−10x4+35x3−50x2+24x
Evaluate
x(x−1)(x−2)(x−3)(x−4)
Multiply the terms
More Steps
Evaluate
x(x−1)
Apply the distributive property
x×x−x×1
Multiply the terms
x2−x×1
Any expression multiplied by 1 remains the same
x2−x
(x2−x)(x−2)(x−3)(x−4)
Multiply the terms
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Evaluate
(x2−x)(x−2)
Apply the distributive property
x2×x−x2×2−x×x−(−x×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)
Use the commutative property to reorder the terms
x3−2x2−x×x−(−x×2)
Multiply the terms
x3−2x2−x2−(−x×2)
Use the commutative property to reorder the terms
x3−2x2−x2−(−2x)
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
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
(x3−3x2+2x)(x−3)(x−4)
Multiply the terms
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Evaluate
(x3−3x2+2x)(x−3)
Apply the distributive property
x3×x−x3×3−3x2×x−(−3x2×3)+2x×x−2x×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−x3×3−3x2×x−(−3x2×3)+2x×x−2x×3
Use the commutative property to reorder the terms
x4−3x3−3x2×x−(−3x2×3)+2x×x−2x×3
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
x4−3x3−3x3−(−3x2×3)+2x×x−2x×3
Multiply the numbers
x4−3x3−3x3−(−9x2)+2x×x−2x×3
Multiply the terms
x4−3x3−3x3−(−9x2)+2x2−2x×3
Multiply the numbers
x4−3x3−3x3−(−9x2)+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
x4−3x3−3x3+9x2+2x2−6x
Subtract the terms
More Steps
Evaluate
−3x3−3x3
Collect like terms by calculating the sum or difference of their coefficients
(−3−3)x3
Subtract the numbers
−6x3
x4−6x3+9x2+2x2−6x
Add the terms
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Evaluate
9x2+2x2
Collect like terms by calculating the sum or difference of their coefficients
(9+2)x2
Add the numbers
11x2
x4−6x3+11x2−6x
(x4−6x3+11x2−6x)(x−4)
Apply the distributive property
x4×x−x4×4−6x3×x−(−6x3×4)+11x2×x−11x2×4−6x×x−(−6x×4)
Multiply the terms
More Steps
Evaluate
x4×x
Use the product rule an×am=an+m to simplify the expression
x4+1
Add the numbers
x5
x5−x4×4−6x3×x−(−6x3×4)+11x2×x−11x2×4−6x×x−(−6x×4)
Use the commutative property to reorder the terms
x5−4x4−6x3×x−(−6x3×4)+11x2×x−11x2×4−6x×x−(−6x×4)
Multiply the terms
More Steps
Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
x5−4x4−6x4−(−6x3×4)+11x2×x−11x2×4−6x×x−(−6x×4)
Multiply the numbers
x5−4x4−6x4−(−24x3)+11x2×x−11x2×4−6x×x−(−6x×4)
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
x5−4x4−6x4−(−24x3)+11x3−11x2×4−6x×x−(−6x×4)
Multiply the numbers
x5−4x4−6x4−(−24x3)+11x3−44x2−6x×x−(−6x×4)
Multiply the terms
x5−4x4−6x4−(−24x3)+11x3−44x2−6x2−(−6x×4)
Multiply the numbers
x5−4x4−6x4−(−24x3)+11x3−44x2−6x2−(−24x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x5−4x4−6x4+24x3+11x3−44x2−6x2+24x
Subtract the terms
More Steps
Evaluate
−4x4−6x4
Collect like terms by calculating the sum or difference of their coefficients
(−4−6)x4
Subtract the numbers
−10x4
x5−10x4+24x3+11x3−44x2−6x2+24x
Add the terms
More Steps
Evaluate
24x3+11x3
Collect like terms by calculating the sum or difference of their coefficients
(24+11)x3
Add the numbers
35x3
x5−10x4+35x3−44x2−6x2+24x
Solution
More Steps
Evaluate
−44x2−6x2
Collect like terms by calculating the sum or difference of their coefficients
(−44−6)x2
Subtract the numbers
−50x2
x5−10x4+35x3−50x2+24x
Show Solution
Find the roots
x1=0,x2=1,x3=2,x4=3,x5=4
Evaluate
x(x−1)(x−2)(x−3)(x−4)
To find the roots of the expression,set the expression equal to 0
x(x−1)(x−2)(x−3)(x−4)=0
Separate the equation into 5 possible cases
x=0x−1=0x−2=0x−3=0x−4=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−2=0x−3=0x−4=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=1x=2x−3=0x−4=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=2x=3x−4=0
Solve the equation
More Steps
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=0x=1x=2x=3x=4
Solution
x1=0,x2=1,x3=2,x4=3,x5=4
Show Solution