resolve into factor: p^4+10p^2+9
Answers
Answer:
p = {-1, 1, -3, 3}
Step-by-step explanation:
Simplifying
p4 + -10p2 + 9 = 0
Reorder the terms:
9 + -10p2 + p4 = 0
Solving
9 + -10p2 + p4 = 0
Solving for variable 'p'.
Factor a trinomial.
(1 + -1p2)(9 + -1p2) = 0
Factor a difference between two squares.
((1 + p)(1 + -1p))(9 + -1p2) = 0
Factor a difference between two squares.
((3 + p)(3 + -1p))(1 + p)(1 + -1p) = 0
Subproblem 1
Set the factor '(1 + p)' equal to zero and attempt to solve:
Simplifying
1 + p = 0
Solving
1 + p = 0
Move all terms containing p to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + p = 0 + -1
Combine like terms: 1 + -1 = 0
0 + p = 0 + -1
p = 0 + -1
Combine like terms: 0 + -1 = -1
p = -1
Simplifying
p = -1
Subproblem 2
Set the factor '(1 + -1p)' equal to zero and attempt to solve:
Simplifying
1 + -1p = 0
Solving
1 + -1p = 0
Move all terms containing p to the left, all other terms to the right.
Add '-1' to each side of the equation.
1 + -1 + -1p = 0 + -1
Combine like terms: 1 + -1 = 0
0 + -1p = 0 + -1
-1p = 0 + -1
Combine like terms: 0 + -1 = -1
-1p = -1
Divide each side by '-1'.
p = 1
Simplifying
p = 1
Subproblem 3
Set the factor '(3 + p)' equal to zero and attempt to solve:
Simplifying
3 + p = 0
Solving
3 + p = 0
Move all terms containing p to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + p = 0 + -3
Combine like terms: 3 + -3 = 0
0 + p = 0 + -3
p = 0 + -3
Combine like terms: 0 + -3 = -3
p = -3
Simplifying
p = -3
Subproblem 4
Set the factor '(3 + -1p)' equal to zero and attempt to solve:
Simplifying
3 + -1p = 0
Solving
3 + -1p = 0
Move all terms containing p to the left, all other terms to the right.
Add '-3' to each side of the equation.
3 + -3 + -1p = 0 + -3
Combine like terms: 3 + -3 = 0
0 + -1p = 0 + -3
-1p = 0 + -3
Combine like terms: 0 + -3 = -3
-1p = -3
Divide each side by '-1'.
p = 3
Simplifying
p = 3
Solution
p = {-1, 1, -3, 3}