Question
Simplify the expression
3x4−12x3+9x2
Evaluate
3(x−3)(x−1)x2
Multiply the terms
3x2(x−3)(x−1)
Multiply the terms
More Steps

Evaluate
3x2(x−3)
Apply the distributive property
3x2×x−3x2×3
Multiply the terms
More Steps

Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
3x3−3x2×3
Multiply the numbers
3x3−9x2
(3x3−9x2)(x−1)
Apply the distributive property
3x3×x−3x3×1−9x2×x−(−9x2×1)
Multiply the terms
More Steps

Evaluate
x3×x
Use the product rule an×am=an+m to simplify the expression
x3+1
Add the numbers
x4
3x4−3x3×1−9x2×x−(−9x2×1)
Any expression multiplied by 1 remains the same
3x4−3x3−9x2×x−(−9x2×1)
Multiply the terms
More Steps

Evaluate
x2×x
Use the product rule an×am=an+m to simplify the expression
x2+1
Add the numbers
x3
3x4−3x3−9x3−(−9x2×1)
Any expression multiplied by 1 remains the same
3x4−3x3−9x3−(−9x2)
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
3x4−3x3−9x3+9x2
Solution
More Steps

Evaluate
−3x3−9x3
Collect like terms by calculating the sum or difference of their coefficients
(−3−9)x3
Subtract the numbers
−12x3
3x4−12x3+9x2
Show Solution

Find the roots
x1=0,x2=1,x3=3
Evaluate
3(x−3)(x−1)(x2)
To find the roots of the expression,set the expression equal to 0
3(x−3)(x−1)(x2)=0
Calculate
3(x−3)(x−1)x2=0
Multiply the terms
3x2(x−3)(x−1)=0
Elimination the left coefficient
x2(x−3)(x−1)=0
Separate the equation into 3 possible cases
x2=0x−3=0x−1=0
The only way a power can be 0 is when the base equals 0
x=0x−3=0x−1=0
Solve the equation
More Steps

Evaluate
x−3=0
Move the constant to the right-hand side and change its sign
x=0+3
Removing 0 doesn't change the value,so remove it from the expression
x=3
x=0x=3x−1=0
Solve the equation
More Steps

Evaluate
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=0x=3x=1
Solution
x1=0,x2=1,x3=3
Show Solution
