Question
Simplify the expression
3x5−198x4+1116x3−2184x2+1440x
Evaluate
(3x2−12x×15)(x−2)3
Multiply the terms
(3x2−180x)(x−2)3
Expand the expression
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Evaluate
(x−2)3
Use (a−b)3=a3−3a2b+3ab2−b3 to expand the expression
x3−3x2×2+3x×22−23
Calculate
x3−6x2+12x−8
(3x2−180x)(x3−6x2+12x−8)
Apply the distributive property
3x2×x3−3x2×6x2+3x2×12x−3x2×8−180x×x3−(−180x×6x2)−180x×12x−(−180x×8)
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
3x5−3x2×6x2+3x2×12x−3x2×8−180x×x3−(−180x×6x2)−180x×12x−(−180x×8)
Multiply the terms
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Evaluate
3x2×6x2
Multiply the numbers
18x2×x2
Multiply the terms
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Evaluate
x2×x2
Use the product rule an×am=an+m to simplify the expression
x2+2
Add the numbers
x4
18x4
3x5−18x4+3x2×12x−3x2×8−180x×x3−(−180x×6x2)−180x×12x−(−180x×8)
Multiply the terms
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Evaluate
3x2×12x
Multiply the numbers
36x2×x
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
36x3
3x5−18x4+36x3−3x2×8−180x×x3−(−180x×6x2)−180x×12x−(−180x×8)
Multiply the numbers
3x5−18x4+36x3−24x2−180x×x3−(−180x×6x2)−180x×12x−(−180x×8)
Multiply the terms
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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
3x5−18x4+36x3−24x2−180x4−(−180x×6x2)−180x×12x−(−180x×8)
Multiply the terms
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Evaluate
−180x×6x2
Multiply the numbers
−1080x×x2
Multiply the terms
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Evaluate
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
−1080x3
3x5−18x4+36x3−24x2−180x4−(−1080x3)−180x×12x−(−180x×8)
Multiply the terms
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Evaluate
−180x×12x
Multiply the numbers
−2160x×x
Multiply the terms
−2160x2
3x5−18x4+36x3−24x2−180x4−(−1080x3)−2160x2−(−180x×8)
Multiply the numbers
3x5−18x4+36x3−24x2−180x4−(−1080x3)−2160x2−(−1440x)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
3x5−18x4+36x3−24x2−180x4+1080x3−2160x2+1440x
Subtract the terms
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Evaluate
−18x4−180x4
Collect like terms by calculating the sum or difference of their coefficients
(−18−180)x4
Subtract the numbers
−198x4
3x5−198x4+36x3−24x2+1080x3−2160x2+1440x
Add the terms
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Evaluate
36x3+1080x3
Collect like terms by calculating the sum or difference of their coefficients
(36+1080)x3
Add the numbers
1116x3
3x5−198x4+1116x3−24x2−2160x2+1440x
Solution
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Evaluate
−24x2−2160x2
Collect like terms by calculating the sum or difference of their coefficients
(−24−2160)x2
Subtract the numbers
−2184x2
3x5−198x4+1116x3−2184x2+1440x
Show Solution

Factor the expression
3x(x−60)(x−2)3
Evaluate
(3x2−12x×15)(x−2)3
Multiply the terms
(3x2−180x)(x−2)3
Solution
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Evaluate
3x2−180x
Rewrite the expression
3x×x−3x×60
Factor out 3x from the expression
3x(x−60)
3x(x−60)(x−2)3
Show Solution

Find the roots
x1=0,x2=2,x3=60
Evaluate
(3x2−12x×15)(x−2)3
To find the roots of the expression,set the expression equal to 0
(3x2−12x×15)(x−2)3=0
Multiply the terms
(3x2−180x)(x−2)3=0
Separate the equation into 2 possible cases
3x2−180x=0(x−2)3=0
Solve the equation
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Evaluate
3x2−180x=0
Factor the expression
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Evaluate
3x2−180x
Rewrite the expression
3x×x−3x×60
Factor out 3x from the expression
3x(x−60)
3x(x−60)=0
When the product of factors equals 0,at least one factor is 0
3x=0x−60=0
Solve the equation for x
x=0x−60=0
Solve the equation for x
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Evaluate
x−60=0
Move the constant to the right-hand side and change its sign
x=0+60
Removing 0 doesn't change the value,so remove it from the expression
x=60
x=0x=60
x=0x=60(x−2)3=0
Solve the equation
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Evaluate
(x−2)3=0
The only way a power can be 0 is when the base equals 0
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=60x=2
Solution
x1=0,x2=2,x3=60
Show Solution
