Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
4z3+2z2−2z5
Evaluate
(4z3−2z2−4z5)−(−4z2−2z5)
Remove the parentheses
4z3−2z2−4z5−(−4z2−2z5)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
4z3−2z2−4z5+4z2+2z5
Add the terms
More Steps
Evaluate
−2z2+4z2
Collect like terms by calculating the sum or difference of their coefficients
(−2+4)z2
Add the numbers
2z2
4z3+2z2−4z5+2z5
Solution
More Steps
Evaluate
−4z5+2z5
Collect like terms by calculating the sum or difference of their coefficients
(−4+2)z5
Add the numbers
−2z5
4z3+2z2−2z5
Show Solution
Factor the expression
−2z2(1+z)(z2−z−1)
Evaluate
(4z3−2z2−4z5)−(−4z2−2z5)
Remove the parentheses
4z3−2z2−4z5−(−4z2−2z5)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
4z3−2z2−4z5+4z2+2z5
Add the terms
More Steps
Evaluate
−2z2+4z2
Collect like terms by calculating the sum or difference of their coefficients
(−2+4)z2
Add the numbers
2z2
4z3+2z2−4z5+2z5
Add the terms
More Steps
Evaluate
−4z5+2z5
Collect like terms by calculating the sum or difference of their coefficients
(−4+2)z5
Add the numbers
−2z5
4z3+2z2−2z5
Rewrite the expression
−2z2(−2z)+2z2−2z2×z3
Factor out −2z2 from the expression
−2z2(−2z−1+z3)
Solution
More Steps
Evaluate
−2z−1+z3
Calculate
z2−z−1+z3−z2−z
Rewrite the expression
z2−z−1+z×z2−z×z−z
Factor out z from the expression
z2−z−1+z(z2−z−1)
Factor out z2−z−1 from the expression
(1+z)(z2−z−1)
−2z2(1+z)(z2−z−1)
Show Solution
Find the roots
z1=−1,z2=21−5,z3=0,z4=21+5
Alternative Form
z1=−1,z2≈−0.618034,z3=0,z4≈1.618034
Evaluate
(4z3−2z2−4z5)−(−4z2−2z5)
To find the roots of the expression,set the expression equal to 0
(4z3−2z2−4z5)−(−4z2−2z5)=0
Remove the parentheses
4z3−2z2−4z5−(−4z2−2z5)=0
Subtract the terms
More Steps
Simplify
4z3−2z2−4z5−(−4z2−2z5)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
4z3−2z2−4z5+4z2+2z5
Add the terms
More Steps
Evaluate
−2z2+4z2
Collect like terms by calculating the sum or difference of their coefficients
(−2+4)z2
Add the numbers
2z2
4z3+2z2−4z5+2z5
Add the terms
More Steps
Evaluate
−4z5+2z5
Collect like terms by calculating the sum or difference of their coefficients
(−4+2)z5
Add the numbers
−2z5
4z3+2z2−2z5
4z3+2z2−2z5=0
Factor the expression
−2z2(1+z)(z2−z−1)=0
Divide both sides
z2(1+z)(z2−z−1)=0
Separate the equation into 3 possible cases
z2=01+z=0z2−z−1=0
The only way a power can be 0 is when the base equals 0
z=01+z=0z2−z−1=0
Solve the equation
More Steps
Evaluate
1+z=0
Move the constant to the right-hand side and change its sign
z=0−1
Removing 0 doesn't change the value,so remove it from the expression
z=−1
z=0z=−1z2−z−1=0
Solve the equation
More Steps
Evaluate
z2−z−1=0
Substitute a=1,b=−1 and c=−1 into the quadratic formula z=2a−b±b2−4ac
z=21±(−1)2−4(−1)
Simplify the expression
More Steps
Evaluate
(−1)2−4(−1)
Evaluate the power
1−4(−1)
Simplify
1−(−4)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
1+4
Add the numbers
5
z=21±5
Separate the equation into 2 possible cases
z=21+5z=21−5
z=0z=−1z=21+5z=21−5
Solution
z1=−1,z2=21−5,z3=0,z4=21+5
Alternative Form
z1=−1,z2≈−0.618034,z3=0,z4≈1.618034
Show Solution