Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−4z3−2z4
Evaluate
5z3−2z4−9z2×z
Multiply
More Steps
Multiply the terms
−9z2×z
Multiply the terms with the same base by adding their exponents
−9z2+1
Add the numbers
−9z3
5z3−2z4−9z3
Solution
More Steps
Evaluate
5z3−9z3
Collect like terms by calculating the sum or difference of their coefficients
(5−9)z3
Subtract the numbers
−4z3
−4z3−2z4
Show Solution
Factor the expression
−2z3(2+z)
Evaluate
5z3−2z4−9z2×z
Multiply
More Steps
Multiply the terms
9z2×z
Multiply the terms with the same base by adding their exponents
9z2+1
Add the numbers
9z3
5z3−2z4−9z3
Subtract the terms
More Steps
Evaluate
5z3−9z3
Collect like terms by calculating the sum or difference of their coefficients
(5−9)z3
Subtract the numbers
−4z3
−4z3−2z4
Rewrite the expression
−2z3×2−2z3×z
Solution
−2z3(2+z)
Show Solution
Find the roots
z1=−2,z2=0
Evaluate
5z3−2z4−9z2×z
To find the roots of the expression,set the expression equal to 0
5z3−2z4−9z2×z=0
Multiply
More Steps
Multiply the terms
9z2×z
Multiply the terms with the same base by adding their exponents
9z2+1
Add the numbers
9z3
5z3−2z4−9z3=0
Subtract the terms
More Steps
Simplify
5z3−2z4−9z3
Subtract the terms
More Steps
Evaluate
5z3−9z3
Collect like terms by calculating the sum or difference of their coefficients
(5−9)z3
Subtract the numbers
−4z3
−4z3−2z4
−4z3−2z4=0
Factor the expression
−2z3(2+z)=0
Divide both sides
z3(2+z)=0
Separate the equation into 2 possible cases
z3=02+z=0
The only way a power can be 0 is when the base equals 0
z=02+z=0
Solve the equation
More Steps
Evaluate
2+z=0
Move the constant to the right-hand side and change its sign
z=0−2
Removing 0 doesn't change the value,so remove it from the expression
z=−2
z=0z=−2
Solution
z1=−2,z2=0
Show Solution