Algebra
Calculus
Trigonometry
Matrix
Question
Solve the inequality
Solve the inequality by testing the values in the interval
Solve the inequality by separating into cases
Solve for p
p∈(−∞,−1)∪(2,+∞)
Evaluate
p2−p−2>0
Rewrite the expression
p2−p−2=0
Factor the expression
More Steps
Evaluate
p2−p−2
Rewrite the expression
p2+(1−2)p−2
Calculate
p2+p−2p−2
Rewrite the expression
p×p+p−2p−2
Factor out p from the expression
p(p+1)−2p−2
Factor out −2 from the expression
p(p+1)−2(p+1)
Factor out p+1 from the expression
(p−2)(p+1)
(p−2)(p+1)=0
When the product of factors equals 0,at least one factor is 0
p−2=0p+1=0
Solve the equation for p
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Evaluate
p−2=0
Move the constant to the right-hand side and change its sign
p=0+2
Removing 0 doesn't change the value,so remove it from the expression
p=2
p=2p+1=0
Solve the equation for p
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Evaluate
p+1=0
Move the constant to the right-hand side and change its sign
p=0−1
Removing 0 doesn't change the value,so remove it from the expression
p=−1
p=2p=−1
Determine the test intervals using the critical values
p<−1−1<p<2p>2
Choose a value form each interval
p1=−2p2=1p3=3
To determine if p<−1 is the solution to the inequality,test if the chosen value p=−2 satisfies the initial inequality
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Evaluate
(−2)2−(−2)−2>0
Subtract the numbers
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Evaluate
(−2)2−(−2)−2
Evaluate the power
4−(−2)−2
Subtract the terms
6−2
Subtract the numbers
4
4>0
Check the inequality
true
p<−1 is the solutionp2=1p3=3
To determine if −1<p<2 is the solution to the inequality,test if the chosen value p=1 satisfies the initial inequality
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Evaluate
12−1−2>0
Simplify
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Evaluate
12−1−2
1 raised to any power equals to 1
1−1−2
Apply the inverse property of addition
−2
−2>0
Check the inequality
false
p<−1 is the solution−1<p<2 is not a solutionp3=3
To determine if p>2 is the solution to the inequality,test if the chosen value p=3 satisfies the initial inequality
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Evaluate
32−3−2>0
Subtract the numbers
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Evaluate
32−3−2
Evaluate the power
9−3−2
Subtract the numbers
4
4>0
Check the inequality
true
p<−1 is the solution−1<p<2 is not a solutionp>2 is the solution
Solution
p∈(−∞,−1)∪(2,+∞)
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