Question
Factor the expression
Factor
(2p−1)(5p+2)
Evaluate
10p2−p−2
Rewrite the expression
10p2+(4−5)p−2
Calculate
10p2+4p−5p−2
Rewrite the expression
2p×5p+2p×2−5p−2
Factor out 2p from the expression
2p(5p+2)−5p−2
Factor out −1 from the expression
2p(5p+2)−(5p+2)
Solution
(2p−1)(5p+2)
Show Solution
Find the roots
Find the roots of the algebra expression
p1=−52,p2=21
Alternative Form
p1=−0.4,p2=0.5
Evaluate
10p2−p−2
To find the roots of the expression,set the expression equal to 0
10p2−p−2=0
Factor the expression
More Steps
Evaluate
10p2−p−2
Rewrite the expression
10p2+(4−5)p−2
Calculate
10p2+4p−5p−2
Rewrite the expression
2p×5p+2p×2−5p−2
Factor out 2p from the expression
2p(5p+2)−5p−2
Factor out −1 from the expression
2p(5p+2)−(5p+2)
Factor out 5p+2 from the expression
(2p−1)(5p+2)
(2p−1)(5p+2)=0
When the product of factors equals 0,at least one factor is 0
2p−1=05p+2=0
Solve the equation for p
More Steps
Evaluate
2p−1=0
Move the constant to the right-hand side and change its sign
2p=0+1
Removing 0 doesn't change the value,so remove it from the expression
2p=1
Divide both sides
22p=21
Divide the numbers
p=21
p=215p+2=0
Solve the equation for p
More Steps
Evaluate
5p+2=0
Move the constant to the right-hand side and change its sign
5p=0−2
Removing 0 doesn't change the value,so remove it from the expression
5p=−2
Divide both sides
55p=5−2
Divide the numbers
p=5−2
Use b−a=−ba=−ba to rewrite the fraction
p=−52
p=21p=−52
Solution
p1=−52,p2=21
Alternative Form
p1=−0.4,p2=0.5
Show Solution