Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x5−25x3−x2+25
Evaluate
(x3−1)(x2−25)
Apply the distributive property
x3×x2−x3×25−x2−(−25)
Multiply the terms
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Evaluate
x3×x2
Use the product rule an×am=an+m to simplify the expression
x3+2
Add the numbers
x5
x5−x3×25−x2−(−25)
Use the commutative property to reorder the terms
x5−25x3−x2−(−25)
Solution
x5−25x3−x2+25
Show Solution
Factor the expression
(x−1)(x2+x+1)(x−5)(x+5)
Evaluate
(x3−1)(x2−25)
Factor the expression
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Evaluate
x3−1
Calculate
x3+x2+x−x2−x−1
Rewrite the expression
x×x2+x×x+x−x2−x−1
Factor out x from the expression
x(x2+x+1)−x2−x−1
Factor out −1 from the expression
x(x2+x+1)−(x2+x+1)
Factor out x2+x+1 from the expression
(x−1)(x2+x+1)
(x−1)(x2+x+1)(x2−25)
Solution
(x−1)(x2+x+1)(x−5)(x+5)
Show Solution
Find the roots
x1=−5,x2=1,x3=5
Evaluate
(x3−1)(x2−25)
To find the roots of the expression,set the expression equal to 0
(x3−1)(x2−25)=0
Separate the equation into 2 possible cases
x3−1=0x2−25=0
Solve the equation
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Evaluate
x3−1=0
Move the constant to the right-hand side and change its sign
x3=0+1
Removing 0 doesn't change the value,so remove it from the expression
x3=1
Take the 3-th root on both sides of the equation
3x3=31
Calculate
x=31
Simplify the root
x=1
x=1x2−25=0
Solve the equation
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Evaluate
x2−25=0
Move the constant to the right-hand side and change its sign
x2=0+25
Removing 0 doesn't change the value,so remove it from the expression
x2=25
Take the root of both sides of the equation and remember to use both positive and negative roots
x=±25
Simplify the expression
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Evaluate
25
Write the number in exponential form with the base of 5
52
Reduce the index of the radical and exponent with 2
5
x=±5
Separate the equation into 2 possible cases
x=5x=−5
x=1x=5x=−5
Solution
x1=−5,x2=1,x3=5
Show Solution