Question
Simplify the expression
−31x5+31x4
Evaluate
(−31)(x−1)x4
Remove the parentheses
−31(x−1)x4
Multiply the terms
−31x4(x−1)
Apply the distributive property
−31x4×x−(−31x4×1)
Multiply the terms
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Evaluate
x4×x
Use the product rule an×am=an+m to simplify the expression
x4+1
Add the numbers
x5
−31x5−(−31x4×1)
Any expression multiplied by 1 remains the same
−31x5−(−31x4)
Solution
−31x5+31x4
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Find the roots
x1=0,x2=1
Evaluate
(−31)(x−1)(x4)
To find the roots of the expression,set the expression equal to 0
(−31)(x−1)(x4)=0
Remove the parentheses
−31(x−1)(x4)=0
Calculate
−31(x−1)x4=0
Multiply the terms
−31x4(x−1)=0
Change the sign
31x4(x−1)=0
Elimination the left coefficient
x4(x−1)=0
Separate the equation into 2 possible cases
x4=0x−1=0
The only way a power can be 0 is when the base equals 0
x=0x−1=0
Solve the equation
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Evaluate
x−1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
x=0x=1
Solution
x1=0,x2=1
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