Writing polynomials as a product of linear factors..? x³ + 3x²?
My Equation is:
(sorry I dont know how to do x cubed on my computer)
X^4+5x²-36
I'm thinking I would break it up into:
x^4+9x-4x-36 which would be further broken up into:
x(x³+9)-4(x-9)
Is that even how you would go about solving that sort of problem? And if so, how would I finish it? If it's not what did I do wrong and how what I solve it instead?
More Questions From This User See All
Answers & Comments
Verified answer
x^4 + 5x² - 36 = 0 → let: X = x² → where X ≥ 0
X² + 5X - 36 = 0
Polynomial like: ax² + bx + c, where:
a = 1
b = 5
c = - 36
Δ = b² - 4ac (discriminant)
Δ = 5² - 4(1 * - 36) = 25 + 144 = 169 = 13²
x1 = (- b - √Δ) / 2a = (- 5 - 13) / (2 * 1) = - 18/2 = - 9 → no possible
x2 = (- b + √Δ) / 2a = (- 5 + 13) / (2 * 1) = 8/2 = 4 → you keep only this solution
Recall: x² = X
x² = 4
x = 2 or x = - 2
Solution = { - 2 ; 2 }
(x - 2) (x + 2)(x + 3) Linear aspects skill they'll all be interior the style (x - a) on account that's a cubic, there'll be 3 of them. you are able to element via grouping.. x^2 (x + 3) - 4(x + 3) (x^2 - 4) (x + 3) (x - 2) (x + 2) (x + 3)