Is there any way to transform the equation composed of cubic polynomials into the equation in the form of multiplication of first-order polynomials and second-order polynomials? The equation composed of quadratic polynomials can be transformed into the form of multiplication of two first-order polynomials, and cross multiplication can be used. What about the equation of cubic polynomials? For example, 2x ^ 3-6x ^ 24 = 0 In the example, 4 is preceded by a plus sign

Is there any way to transform the equation composed of cubic polynomials into the equation in the form of multiplication of first-order polynomials and second-order polynomials? The equation composed of quadratic polynomials can be transformed into the form of multiplication of two first-order polynomials, and cross multiplication can be used. What about the equation of cubic polynomials? For example, 2x ^ 3-6x ^ 24 = 0 In the example, 4 is preceded by a plus sign

x^3 - 3x^2 + 2 = 0
x^3 - x^2 - 2x^2 + 4 = 0
x^2(x-1) - 2(x+1)(x-1) = (x-1)(x^2 - 2x - 2) = 0
x = 1,1 + sqrt(3),1- sqrt(3)

If the sum of the polynomials MX ^ 5 + x ^ n + 1 - 2x + 1 and 2x ^ 5 + 4x-5 about X is a quadratic trinomial, then the value of M + n is?
If the sum of N + 1 degree 2x + 1 and 2x ^ 5 + 4x-5 of the polynomial MX ^ 5 + X about X is a quadratic trinomial, then the value of M + n is?

Let the quadratic polynomial of X be ax ^ 2 + BX + C
Then when x = 1
His value = a * 1 ^ 2 + b * 1 + C = a + B + C
Because x is one, the value of the polynomial is - 1
So a + B + C = - 1
The coefficients of this polynomial are a, B and C respectively
So the sum of the coefficients is a + B + C
So the sum of the coefficients of the polynomial is - 1

Known polynomial x ^ 3 + (m-2) x ^ 2 + 4x-1, is about the cubic trinomial of X, find the value of M!

Because it's three
If the coefficients of the cubic term and the first term are determined, the constant term can not be removed
So the coefficient of the quadratic term is 0
If the coefficient of quadratic term m-2 is not zero, it looks like four terms
So m-2 should be equal to 0, that is, M = 2
So the original formula becomes x ^ 3 + 4x-1,
Meet the requirements of cubic trinomial