Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−z49z+45
Evaluate
z5−9z2−45z
Use b−a=−ba=−ba to rewrite the fraction
−z59z2+45z
Factor
−z5z(9z+45)
Solution
More Steps
Calculate
z5z
Use the product rule aman=an−m to simplify the expression
z5−11
Subtract the terms
z41
−z49z+45
Show Solution
Find the excluded values
z=0
Evaluate
z5−9z2−45z
To find the excluded values,set the denominators equal to 0
z5=0
Solution
z=0
Show Solution
Rewrite the fraction
−z445−z39
Evaluate
z5−9z2−45z
For each factor in the denominator,write a new fraction
z5?+z4?+z3?+z2?+z?
Write the terms in the numerator
z5A+z4B+z3C+z2D+zE
Set the sum of fractions equal to the original fraction
z5−9z2−45z=z5A+z4B+z3C+z2D+zE
Multiply both sides
z5−9z2−45z×z5=z5A×z5+z4B×z5+z3C×z5+z2D×z5+zE×z5
Simplify the expression
−9z2−45z=1×A+zB+z2C+z3D+z4E
Any expression multiplied by 1 remains the same
−9z2−45z=A+zB+z2C+z3D+z4E
Group the terms
−9z2−45z=Ez4+Dz3+Cz2+Bz+A
Equate the coefficients
⎩⎨⎧0=E0=D−9=C−45=B0=A
Swap the sides
⎩⎨⎧E=0D=0C=−9B=−45A=0
Find the intersection
⎩⎨⎧A=0B=−45C=−9D=0E=0
Solution
−z445−z39
Show Solution
Find the roots
z=−5
Evaluate
z5−9z2−45z
To find the roots of the expression,set the expression equal to 0
z5−9z2−45z=0
The only way a power can not be 0 is when the base not equals 0
z5−9z2−45z=0,z=0
Calculate
z5−9z2−45z=0
Divide the terms
More Steps
Evaluate
z5−9z2−45z
Use b−a=−ba=−ba to rewrite the fraction
−z59z2+45z
Factor
−z5z(9z+45)
Reduce the fraction
More Steps
Calculate
z5z
Use the product rule aman=an−m to simplify the expression
z5−11
Subtract the terms
z41
−z49z+45
−z49z+45=0
Rewrite the expression
z4−9z−45=0
Cross multiply
−9z−45=z4×0
Simplify the equation
−9z−45=0
Move the constant to the right side
−9z=0+45
Removing 0 doesn't change the value,so remove it from the expression
−9z=45
Change the signs on both sides of the equation
9z=−45
Divide both sides
99z=9−45
Divide the numbers
z=9−45
Divide the numbers
More Steps
Evaluate
9−45
Reduce the numbers
1−5
Calculate
−5
z=−5
Check if the solution is in the defined range
z=−5,z=0
Solution
z=−5
Show Solution