Question
Simplify the expression
x3−7x2+15x−9
Evaluate
(x−1)(x−3)2
Expand the expression
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Evaluate
(x−3)2
Use (a−b)2=a2−2ab+b2 to expand the expression
x2−2x×3+32
Calculate
x2−6x+9
(x−1)(x2−6x+9)
Apply the distributive property
x×x2−x×6x+x×9−x2−(−6x)−9
Multiply the terms
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Evaluate
x×x2
Use the product rule an×am=an+m to simplify the expression
x1+2
Add the numbers
x3
x3−x×6x+x×9−x2−(−6x)−9
Multiply the terms
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Evaluate
x×6x
Use the commutative property to reorder the terms
6x×x
Multiply the terms
6x2
x3−6x2+x×9−x2−(−6x)−9
Use the commutative property to reorder the terms
x3−6x2+9x−x2−(−6x)−9
If a negative sign or a subtraction symbol appears outside parentheses, remove the parentheses and change the sign of every term within the parentheses
x3−6x2+9x−x2+6x−9
Subtract the terms
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Evaluate
−6x2−x2
Collect like terms by calculating the sum or difference of their coefficients
(−6−1)x2
Subtract the numbers
−7x2
x3−7x2+9x+6x−9
Solution
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Evaluate
9x+6x
Collect like terms by calculating the sum or difference of their coefficients
(9+6)x
Add the numbers
15x
x3−7x2+15x−9
Show Solution

Find the roots
x1=1,x2=3
Evaluate
(x−1)(x−3)2
To find the roots of the expression,set the expression equal to 0
(x−1)(x−3)2=0
Separate the equation into 2 possible cases
x−1=0(x−3)2=0
Solve the equation
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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=1(x−3)2=0
Solve the equation
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Evaluate
(x−3)2=0
The only way a power can be 0 is when the base equals 0
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=1x=3
Solution
x1=1,x2=3
Show Solution
