Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(x−2)(x2+2x+3)
Evaluate
x3−x−6
Calculate
x3+2x2+3x−2x2−4x−6
Rewrite the expression
x×x2+x×2x+x×3−2x2−2×2x−2×3
Factor out x from the expression
x(x2+2x+3)−2x2−2×2x−2×3
Factor out −2 from the expression
x(x2+2x+3)−2(x2+2x+3)
Solution
(x−2)(x2+2x+3)
Show Solution
Find the roots
x1=−1−2×i,x2=−1+2×i,x3=2
Alternative Form
x1≈−1−1.414214i,x2≈−1+1.414214i,x3=2
Evaluate
x3−x−6
To find the roots of the expression,set the expression equal to 0
x3−x−6=0
Factor the expression
(x−2)(x2+2x+3)=0
Separate the equation into 2 possible cases
x−2=0x2+2x+3=0
Solve the equation
More Steps
Evaluate
x−2=0
Move the constant to the right-hand side and change its sign
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=2x2+2x+3=0
Solve the equation
More Steps
Evaluate
x2+2x+3=0
Substitute a=1,b=2 and c=3 into the quadratic formula x=2a−b±b2−4ac
x=2−2±22−4×3
Simplify the expression
More Steps
Evaluate
22−4×3
Multiply the numbers
22−12
Evaluate the power
4−12
Subtract the numbers
−8
x=2−2±−8
Simplify the radical expression
More Steps
Evaluate
−8
Evaluate the power
8×−1
Evaluate the power
8×i
Evaluate the power
22×i
x=2−2±22×i
Separate the equation into 2 possible cases
x=2−2+22×ix=2−2−22×i
Simplify the expression
x=−1+2×ix=2−2−22×i
Simplify the expression
x=−1+2×ix=−1−2×i
x=2x=−1+2×ix=−1−2×i
Solution
x1=−1−2×i,x2=−1+2×i,x3=2
Alternative Form
x1≈−1−1.414214i,x2≈−1+1.414214i,x3=2
Show Solution