Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x6−5x5−2x4+x3
Evaluate
(x−5)x5−(2x−1)x3
Multiply the terms
x5(x−5)−(2x−1)x3
Multiply the terms
x5(x−5)−x3(2x−1)
Expand the expression
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Calculate
x5(x−5)
Apply the distributive property
x5×x−x5×5
Multiply the terms
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Evaluate
x5×x
Use the product rule an×am=an+m to simplify the expression
x5+1
Add the numbers
x6
x6−x5×5
Use the commutative property to reorder the terms
x6−5x5
x6−5x5−x3(2x−1)
Solution
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Calculate
−x3(2x−1)
Apply the distributive property
−x3×2x−(−x3×1)
Multiply the terms
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Evaluate
−x3×2x
Multiply the numbers
−2x3×x
Multiply the terms
−2x4
−2x4−(−x3×1)
Any expression multiplied by 1 remains the same
−2x4−(−x3)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−2x4+x3
x6−5x5−2x4+x3
Show Solution
Factor the expression
(x3−5x2−2x+1)x3
Evaluate
(x−5)x5−(2x−1)x3
Multiply the terms
x5(x−5)−(2x−1)x3
Multiply the terms
x5(x−5)−x3(2x−1)
Rewrite the expression
x2(x−5)x3+(−2x+1)x3
Factor out x3 from the expression
(x2(x−5)−2x+1)x3
Solution
(x3−5x2−2x+1)x3
Show Solution
Find the roots
x1≈−0.634609,x2=0,x3≈0.295117,x4≈5.339492
Evaluate
(x−5)(x5)−(2x−1)(x3)
To find the roots of the expression,set the expression equal to 0
(x−5)(x5)−(2x−1)(x3)=0
Calculate
(x−5)x5−(2x−1)(x3)=0
Calculate
(x−5)x5−(2x−1)x3=0
Multiply the terms
x5(x−5)−(2x−1)x3=0
Multiply the terms
x5(x−5)−x3(2x−1)=0
Calculate
More Steps
Evaluate
x5(x−5)−x3(2x−1)
Expand the expression
More Steps
Calculate
x5(x−5)
Apply the distributive property
x5×x−x5×5
Multiply the terms
x6−x5×5
Use the commutative property to reorder the terms
x6−5x5
x6−5x5−x3(2x−1)
Expand the expression
More Steps
Calculate
−x3(2x−1)
Apply the distributive property
−x3×2x−(−x3×1)
Multiply the terms
−2x4−(−x3×1)
Any expression multiplied by 1 remains the same
−2x4−(−x3)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
−2x4+x3
x6−5x5−2x4+x3
x6−5x5−2x4+x3=0
Factor the expression
x3(x3−5x2−2x+1)=0
Separate the equation into 2 possible cases
x3=0x3−5x2−2x+1=0
The only way a power can be 0 is when the base equals 0
x=0x3−5x2−2x+1=0
Solve the equation
x=0x≈5.339492x≈−0.634609x≈0.295117
Solution
x1≈−0.634609,x2=0,x3≈0.295117,x4≈5.339492
Show Solution