give Factors or this polynomial 5x⁴-x³-4x-5=0.
Answers
Answer:Sample problems:
1) x3 + 2x2 - 9x - 18 = 0
x2( x + 2) - 9(x + 2) = 0 group the first two and last two!
(x2 - 9)(x + 2) = 0 Factor out the common factor!
(x - 3)(x + 3)(x + 2) = 0
The solutions are x = 3, x = -3 and x = -2
2) x3 - 4x2 - 9x + 36 = 0
x2(x - 4) - 9(x - 4) = 0 Group the first two and last two!
(x2 - 9)(x - 4) = 0 Take out the common factor!
(x - 3)(x + 3)(x -4) = 0
The solutions are x = 3, x = -3 and x = 4
Quadratic form
Sample problems
1) x4 - 2x2 -3 = 0 This is not a quadratic, but can look like one!
(x2)2 - 2(x2) - 3 = 0 Now looks like a quadratic.
let y = x2 basic substitution
y2 - 2y - 3 = 0 Now it is a quadratic equation!!
(y - 3)(y + 1) = 0 Factoring
This means y = 3 and y = -1
But we don't want to find what y is. Now find x.
3 = x2 or -1 = x2
By taking the square root!
2) x4 + 5x2 + 6 = 0
y = x2 is the substitution again!!
y2 + 5y + 6 = 0
(y + 3)(y + 2) = 0
y = -3 or y = -2
-3 = x2 or -2 = x2
By taking the square root!
Step-by-step explanation: