Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(x−5)(x2+x+1)
Evaluate
x3−4x2−4x−5
Calculate
x3+x2+x−5x2−5x−5
Rewrite the expression
x×x2+x×x+x−5x2−5x−5
Factor out x from the expression
x(x2+x+1)−5x2−5x−5
Factor out −5 from the expression
x(x2+x+1)−5(x2+x+1)
Solution
(x−5)(x2+x+1)
Show Solution
Find the roots
x1=−21−23i,x2=−21+23i,x3=5
Alternative Form
x1≈−0.5−0.866025i,x2≈−0.5+0.866025i,x3=5
Evaluate
x3−4x2−4x−5
To find the roots of the expression,set the expression equal to 0
x3−4x2−4x−5=0
Factor the expression
(x−5)(x2+x+1)=0
Separate the equation into 2 possible cases
x−5=0x2+x+1=0
Solve the equation
More Steps
Evaluate
x−5=0
Move the constant to the right-hand side and change its sign
x=0+5
Removing 0 doesn't change the value,so remove it from the expression
x=5
x=5x2+x+1=0
Solve the equation
More Steps
Evaluate
x2+x+1=0
Substitute a=1,b=1 and c=1 into the quadratic formula x=2a−b±b2−4ac
x=2−1±12−4
Simplify the expression
More Steps
Evaluate
12−4
1 raised to any power equals to 1
1−4
Subtract the numbers
−3
x=2−1±−3
Simplify the radical expression
More Steps
Evaluate
−3
Evaluate the power
3×−1
Evaluate the power
3×i
x=2−1±3×i
Separate the equation into 2 possible cases
x=2−1+3×ix=2−1−3×i
Simplify the expression
x=−21+23ix=2−1−3×i
Simplify the expression
x=−21+23ix=−21−23i
x=5x=−21+23ix=−21−23i
Solution
x1=−21−23i,x2=−21+23i,x3=5
Alternative Form
x1≈−0.5−0.866025i,x2≈−0.5+0.866025i,x3=5
Show Solution