Algebra
Calculus
Trigonometry
Matrix
Question
Factor the expression
3(p−7)(p+2)
Evaluate
3p2−15p−42
Rewrite the expression
3p2−3×5p−3×14
Factor out 3 from the expression
3(p2−5p−14)
Solution
More Steps
Evaluate
p2−5p−14
Rewrite the expression
p2+(2−7)p−14
Calculate
p2+2p−7p−14
Rewrite the expression
p×p+p×2−7p−7×2
Factor out p from the expression
p(p+2)−7p−7×2
Factor out −7 from the expression
p(p+2)−7(p+2)
Factor out p+2 from the expression
(p−7)(p+2)
3(p−7)(p+2)
Show Solution
Find the roots
p1=−2,p2=7
Evaluate
3p2−15p−42
To find the roots of the expression,set the expression equal to 0
3p2−15p−42=0
Factor the expression
More Steps
Evaluate
3p2−15p−42
Rewrite the expression
3p2−3×5p−3×14
Factor out 3 from the expression
3(p2−5p−14)
Factor the expression
More Steps
Evaluate
p2−5p−14
Rewrite the expression
p2+(2−7)p−14
Calculate
p2+2p−7p−14
Rewrite the expression
p×p+p×2−7p−7×2
Factor out p from the expression
p(p+2)−7p−7×2
Factor out −7 from the expression
p(p+2)−7(p+2)
Factor out p+2 from the expression
(p−7)(p+2)
3(p−7)(p+2)
3(p−7)(p+2)=0
Divide the terms
(p−7)(p+2)=0
When the product of factors equals 0,at least one factor is 0
p−7=0p+2=0
Solve the equation for p
More Steps
Evaluate
p−7=0
Move the constant to the right-hand side and change its sign
p=0+7
Removing 0 doesn't change the value,so remove it from the expression
p=7
p=7p+2=0
Solve the equation for p
More Steps
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=7p=−2
Solution
p1=−2,p2=7
Show Solution