Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(x−2)(x−1)2
Evaluate
x3−4x2+5x−2
Calculate
x3−2x2+x−2x2+4x−2
Rewrite the expression
x×x2−x×2x+x−2x2+2×2x−2
Factor out x from the expression
x(x2−2x+1)−2x2+2×2x−2
Factor out −2 from the expression
x(x2−2x+1)−2(x2−2x+1)
Factor out x2−2x+1 from the expression
(x−2)(x2−2x+1)
Solution
(x−2)(x−1)2
Show Solution
Find the roots
x1=1,x2=2
Evaluate
x3−4x2+5x−2
To find the roots of the expression,set the expression equal to 0
x3−4x2+5x−2=0
Factor the expression
(x−2)(x−1)2=0
Separate the equation into 2 possible cases
x−2=0(x−1)2=0
Solve the equation
More Steps
Evaluate
x−2=0
Move the constant to the right side
x=0+2
Removing 0 doesn't change the value,so remove it from the expression
x=2
x=2(x−1)2=0
Solve the equation
More Steps
Evaluate
(x−1)2=0
The only way a power can be 0 is when the base equals 0
x−1=0
Move the constant to the right-hand side and change its sign
x=0+1
Removing 0 doesn't change the value,so remove it from the expression
x=1
x=2x=1
Solution
x1=1,x2=2
Show Solution