Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
(x−2)(x−1)(x+1)(x+4)
Evaluate
x4+2x3−9x2−2x+8
Calculate
x4+4x3−x2−4x−2x3−8x2+2x+8
Rewrite the expression
x×x3+x×4x2−x×x−x×4−2x3−2×4x2+2x+2×4
Factor out x from the expression
x(x3+4x2−x−4)−2x3−2×4x2+2x+2×4
Factor out −2 from the expression
x(x3+4x2−x−4)−2(x3+4x2−x−4)
Factor out x3+4x2−x−4 from the expression
(x−2)(x3+4x2−x−4)
Factor the expression
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Evaluate
x3+4x2−x−4
Rewrite the expression
x2×x+x2×4−x−4
Factor out x2 from the expression
x2(x+4)−x−4
Factor out −1 from the expression
x2(x+4)−(x+4)
Factor out x+4 from the expression
(x2−1)(x+4)
(x−2)(x2−1)(x+4)
Solution
(x−2)(x−1)(x+1)(x+4)
Show Solution
Find the roots
x1=−4,x2=−1,x3=1,x4=2
Evaluate
x4+2x3−9x2−2x+8
To find the roots of the expression,set the expression equal to 0
x4+2x3−9x2−2x+8=0
Factor the expression
(x−2)(x−1)(x+1)(x+4)=0
Separate the equation into 4 possible cases
x−2=0x−1=0x+1=0x+4=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+4=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+4=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+4=0
Solve the equation
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Evaluate
x+4=0
Move the constant to the right-hand side and change its sign
x=0−4
Removing 0 doesn't change the value,so remove it from the expression
x=−4
x=2x=1x=−1x=−4
Solution
x1=−4,x2=−1,x3=1,x4=2
Show Solution