Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(x−2)(x−1)(x+1)(x+3)
Evaluate
x4+x3−7x2−x+6
Calculate
x4+3x3−x2−3x−2x3−6x2+2x+6
Rewrite the expression
x×x3+x×3x2−x×x−x×3−2x3−2×3x2+2x+2×3
Factor out x from the expression
x(x3+3x2−x−3)−2x3−2×3x2+2x+2×3
Factor out −2 from the expression
x(x3+3x2−x−3)−2(x3+3x2−x−3)
Factor out x3+3x2−x−3 from the expression
(x−2)(x3+3x2−x−3)
Factor the expression
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Evaluate
x3+3x2−x−3
Rewrite the expression
x2×x+x2×3−x−3
Factor out x2 from the expression
x2(x+3)−x−3
Factor out −1 from the expression
x2(x+3)−(x+3)
Factor out x+3 from the expression
(x2−1)(x+3)
(x−2)(x2−1)(x+3)
Solution
(x−2)(x−1)(x+1)(x+3)
Show Solution
Find the roots
x1=−3,x2=−1,x3=1,x4=2
Evaluate
x4+x3−7x2−x+6
To find the roots of the expression,set the expression equal to 0
x4+x3−7x2−x+6=0
Factor the expression
(x−2)(x−1)(x+1)(x+3)=0
Separate the equation into 4 possible cases
x−2=0x−1=0x+1=0x+3=0
Solve the equation
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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=2x−1=0x+1=0x+3=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=2x=1x+1=0x+3=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=2x=1x=−1x+3=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=2x=1x=−1x=−3
Solution
x1=−3,x2=−1,x3=1,x4=2
Show Solution