Question
Simplify the expression
x4−8x3+15x2
Evaluate
(x−3)x2(x−5)
Multiply the first two terms
x2(x−3)(x−5)
Multiply the terms
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Evaluate
x2(x−3)
Apply the distributive property
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
x3−x2×3
Use the commutative property to reorder the terms
x3−3x2
(x3−3x2)(x−5)
Apply the distributive property
x3×x−x3×5−3x2×x−(−3x2×5)
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−x3×5−3x2×x−(−3x2×5)
Use the commutative property to reorder the terms
x4−5x3−3x2×x−(−3x2×5)
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
x4−5x3−3x3−(−3x2×5)
Multiply the numbers
x4−5x3−3x3−(−15x2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x4−5x3−3x3+15x2
Solution
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Evaluate
−5x3−3x3
Collect like terms by calculating the sum or difference of their coefficients
(−5−3)x3
Subtract the numbers
−8x3
x4−8x3+15x2
Show Solution

Find the roots
x1=0,x2=3,x3=5
Evaluate
(x−3)(x2)(x−5)
To find the roots of the expression,set the expression equal to 0
(x−3)(x2)(x−5)=0
Calculate
(x−3)x2(x−5)=0
Multiply the first two terms
x2(x−3)(x−5)=0
Separate the equation into 3 possible cases
x2=0x−3=0x−5=0
The only way a power can be 0 is when the base equals 0
x=0x−3=0x−5=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=3x−5=0
Solve the equation
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Evaluate
x−5=0
Move the constant to the right-hand side and change its sign
x=0+5
Removing 0 doesn't change the value,so remove it from the expression
x=5
x=0x=3x=5
Solution
x1=0,x2=3,x3=5
Show Solution
