Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
−f33f2+18f+416
Evaluate
f5−3f4−18f3−16f2×26
Multiply the terms
f5−3f4−18f3−416f2
Use b−a=−ba=−ba to rewrite the fraction
−f53f4+18f3+416f2
Factor
−f5f2(3f2+18f+416)
Solution
More Steps
Calculate
f5f2
Use the product rule aman=an−m to simplify the expression
f5−21
Subtract the terms
f31
−f33f2+18f+416
Show Solution
Find the excluded values
f=0
Evaluate
f5−3f4−18f3−16f2×26
To find the excluded values,set the denominators equal to 0
f5=0
Solution
f=0
Show Solution
Rewrite the fraction
−f3416−f218−f3
Evaluate
f5−3f4−18f3−16f2×26
Evaluate
f5−3f4−18f3−416f2
For each factor in the denominator,write a new fraction
f5?+f4?+f3?+f2?+f?
Write the terms in the numerator
f5A+f4B+f3C+f2D+fE
Set the sum of fractions equal to the original fraction
f5−3f4−18f3−416f2=f5A+f4B+f3C+f2D+fE
Multiply both sides
f5−3f4−18f3−416f2×f5=f5A×f5+f4B×f5+f3C×f5+f2D×f5+fE×f5
Simplify the expression
−3f4−18f3−416f2=1×A+fB+f2C+f3D+f4E
Any expression multiplied by 1 remains the same
−3f4−18f3−416f2=A+fB+f2C+f3D+f4E
Group the terms
−3f4−18f3−416f2=Ef4+Df3+Cf2+Bf+A
Equate the coefficients
⎩⎨⎧−3=E−18=D−416=C0=B0=A
Swap the sides
⎩⎨⎧E=−3D=−18C=−416B=0A=0
Find the intersection
⎩⎨⎧A=0B=0C=−416D=−18E=−3
Solution
−f3416−f218−f3
Show Solution
Find the roots
f∈/R
Evaluate
f5−3f4−18f3−16f2×26
To find the roots of the expression,set the expression equal to 0
f5−3f4−18f3−16f2×26=0
The only way a power can not be 0 is when the base not equals 0
f5−3f4−18f3−16f2×26=0,f=0
Calculate
f5−3f4−18f3−16f2×26=0
Multiply the terms
f5−3f4−18f3−416f2=0
Divide the terms
More Steps
Evaluate
f5−3f4−18f3−416f2
Use b−a=−ba=−ba to rewrite the fraction
−f53f4+18f3+416f2
Factor
−f5f2(3f2+18f+416)
Reduce the fraction
More Steps
Calculate
f5f2
Use the product rule aman=an−m to simplify the expression
f5−21
Subtract the terms
f31
−f33f2+18f+416
−f33f2+18f+416=0
Rewrite the expression
f3−3f2−18f−416=0
Cross multiply
−3f2−18f−416=f3×0
Simplify the equation
−3f2−18f−416=0
Multiply both sides
3f2+18f+416=0
Substitute a=3,b=18 and c=416 into the quadratic formula f=2a−b±b2−4ac
f=2×3−18±182−4×3×416
Simplify the expression
f=6−18±182−4×3×416
Simplify the expression
More Steps
Evaluate
182−4×3×416
Multiply the terms
More Steps
Multiply the terms
4×3×416
Multiply the terms
12×416
Multiply the numbers
4992
182−4992
Evaluate the power
324−4992
Subtract the numbers
−4668
f=6−18±−4668
Solution
f∈/R
Show Solution