Algebra
Calculus
Trigonometry
Matrix
Question
Simplify the expression
x4−24x5−4x3
Evaluate
x4−4x3×6x2−4x3
Solution
More Steps
Evaluate
−4x3×6x2
Multiply the terms
−24x3×x2
Multiply the terms with the same base by adding their exponents
−24x3+2
Add the numbers
−24x5
x4−24x5−4x3
Show Solution
Factor the expression
x3(x−24x2−4)
Evaluate
x4−4x3×6x2−4x3
Multiply
More Steps
Evaluate
4x3×6x2
Multiply the terms
24x3×x2
Multiply the terms with the same base by adding their exponents
24x3+2
Add the numbers
24x5
x4−24x5−4x3
Rewrite the expression
x3×x−x3×24x2−x3×4
Solution
x3(x−24x2−4)
Show Solution
Find the roots
x1=481−48383i,x2=481+48383i,x3=0
Alternative Form
x1≈0.02083˙−0.407716i,x2≈0.02083˙+0.407716i,x3=0
Evaluate
x4−4x3×6x2−4x3
To find the roots of the expression,set the expression equal to 0
x4−4x3×6x2−4x3=0
Multiply
More Steps
Multiply the terms
4x3×6x2
Multiply the terms
24x3×x2
Multiply the terms with the same base by adding their exponents
24x3+2
Add the numbers
24x5
x4−24x5−4x3=0
Factor the expression
x3(x−24x2−4)=0
Separate the equation into 2 possible cases
x3=0x−24x2−4=0
The only way a power can be 0 is when the base equals 0
x=0x−24x2−4=0
Solve the equation
More Steps
Evaluate
x−24x2−4=0
Rewrite in standard form
−24x2+x−4=0
Multiply both sides
24x2−x+4=0
Substitute a=24,b=−1 and c=4 into the quadratic formula x=2a−b±b2−4ac
x=2×241±(−1)2−4×24×4
Simplify the expression
x=481±(−1)2−4×24×4
Simplify the expression
More Steps
Evaluate
(−1)2−4×24×4
Evaluate the power
1−4×24×4
Multiply the terms
1−384
Subtract the numbers
−383
x=481±−383
Simplify the radical expression
More Steps
Evaluate
−383
Evaluate the power
383×−1
Evaluate the power
383×i
x=481±383×i
Separate the equation into 2 possible cases
x=481+383×ix=481−383×i
Simplify the expression
x=481+48383ix=481−383×i
Simplify the expression
x=481+48383ix=481−48383i
x=0x=481+48383ix=481−48383i
Solution
x1=481−48383i,x2=481+48383i,x3=0
Alternative Form
x1≈0.02083˙−0.407716i,x2≈0.02083˙+0.407716i,x3=0
Show Solution