Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
5x4−135x3
Evaluate
5x2(x2−3x×9)
Multiply the terms
5x2(x2−27x)
Apply the distributive property
5x2×x2−5x2×27x
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
5x4−5x2×27x
Solution
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Evaluate
5x2×27x
Multiply the numbers
135x2×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
135x3
5x4−135x3
Show Solution
Factor the expression
5x3(x−27)
Evaluate
5x2(x2−3x×9)
Multiply the terms
5x2(x2−27x)
Factor the expression
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Evaluate
x2−27x
Rewrite the expression
x×x−x×27
Factor out x from the expression
x(x−27)
5x2×x(x−27)
Solution
5x3(x−27)
Show Solution
Find the roots
x1=0,x2=27
Evaluate
(5x2)(x2−3x×9)
To find the roots of the expression,set the expression equal to 0
(5x2)(x2−3x×9)=0
Multiply the terms
5x2(x2−3x×9)=0
Multiply the terms
5x2(x2−27x)=0
Elimination the left coefficient
x2(x2−27x)=0
Separate the equation into 2 possible cases
x2=0x2−27x=0
The only way a power can be 0 is when the base equals 0
x=0x2−27x=0
Solve the equation
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Evaluate
x2−27x=0
Factor the expression
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Evaluate
x2−27x
Rewrite the expression
x×x−x×27
Factor out x from the expression
x(x−27)
x(x−27)=0
When the product of factors equals 0,at least one factor is 0
x=0x−27=0
Solve the equation for x
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Evaluate
x−27=0
Move the constant to the right-hand side and change its sign
x=0+27
Removing 0 doesn't change the value,so remove it from the expression
x=27
x=0x=27
x=0x=0x=27
Find the union
x=0x=27
Solution
x1=0,x2=27
Show Solution