A mathematical factorization problem X ^ 8 + x ^ 6 + x ^ 4 + x ^ 2 + X + 1. Remember, it's factorization!

A mathematical factorization problem X ^ 8 + x ^ 6 + x ^ 4 + x ^ 2 + X + 1. Remember, it's factorization!

X ^ 8 + x ^ 6 + x ^ 4 + x ^ 2 + X + 1 = (x ^ 8 + x ^ 6 + x ^ 4) + (x ^ 2 + X + 1) = (x ^ 8 + 2x ^ 6 + x ^ 4-x ^ 6) + (x ^ 2 + X + 1) = x ^ 4 ((x ^ 2 + 1) ^ 2-x ^ 2) + (x ^ 2 + X + 1) = x ^ 4 (x ^ 2 + X + 1) (x ^ 2-x + 1) + (x ^ 2 + X + 1) = (x ^ 6-x ^ 5 + x ^ 4 + 1) (x ^ 2 + X + 1) no difficulty, come on!
What does x ^ 8 mean? It's easy to understand when you know
x^8+x^6+x^4+x^2+x+1
=(x^8+x^6+x^4)+(x^2+x+1)
=(x^8+2x^6+x^4-x^6)+(x^2+x+1)
=x^4((x^2+1)^2-x^2)+(x^2+x+1)
=x^4(x^2+x+1)(x^2-x+1)+(x^2+x+1)
=(x^6-x^5+x^4+1)(x^2+x+1)
(x^8+x^6+x^4+x^2+1)
=(x^2-1)(x^8+x^6+x^4+x^2+1)/(x^2-1)
=(x^10-1)/(x^2-1)
=(x^5+1)(x^5-1)/(x^2-1)
=(x+1)(x^4+x^3-x+1)(x-1)(x^4+x^3+x^2+x+1)/(x^2-1)
=(x^4+x^3-x+1)(x^4+x^3+x^2+x+1)
The general form of practical problem of quadratic equation with one variable: if 2 is a root of equation x * - C = 0, then what is the length C?
What are the other roots?
Since the root takes 2 into C = 4 and X * - 4 = 0, we get (x + 2) multiplied by (X-2) = 0, so the other is followed by - 2
Four
The equation 3x (x-1) = 5 (x + 2) is transformed into a general formula of quadratic equation with one variable______ .
The equation 3x (x-1) = 5 (x + 2) is reduced to a general form of 3x2-8x-10 = 0
If n (n ≠ 0) is the root of the equation x2 + MX + 2n = 0, then the value of M + n is ()
A. 1B. 2C. -1D. -2
∵ n (n ≠ 0) is the root of the equation x2 + MX + 2n = 0 about X. substituting it into N 2 + Mn + 2n = 0, ∵ n ≠ 0, dividing both sides of the equation by N, we get n + m + 2 = 0, ∵ m + n = - 2
Distribution of roots of quadratic equation with one variable
Find the value range of real number m so that the equation about X is x-square + (m-1) x-2m + 1 = 0
There is at least one problem
Problem 2 has at most one positive root
Please write down the conditions, such as △ should be greater than 0, and then solve them
Thank you
Using the inverse method
1 has roots, but only negative roots or 0 roots
M = 1 / 2 but no negative root
If △ > = 0 and - (m-1) 0 only have negative roots
unsolvable
So no matter what the value of M is, it has at least one positive root
Both are positive root times
There are (△ 0-1) > 0-2m
The solution is - 3 + 2 root sign 3
9.5 & # 178; + 9.5 + 0.25 (calculated by simple method)
9.5^2+9.5+0.25
=9.5^2+2*0.5*9.5+0.5^2
=(9.5+0.5)^2
=10^2
=100
How to calculate that the square of parabola y = x and y = 3x + B have only one common point B is equal to
y=x²=3x+b
x²-3x-b=0
If there is only one common point, the equation has only one solution
So the discriminant is equal to 0
9+4b=0
b=9/4
On the junior high school equation solving skills and formulas
Who can send ah ~ all a little can see clearly the best!
First, observe the structure of the equation. If it is very complex, see if you can simplify it by substitution or factorization (in higher order, see if there are any special roots, such as plus or minus 1, plus or minus 2, and extract a common factor)
Factorization mathematics of grade two
(A & sup2; b-2ab & sup2; - B & sup2;) △ B - (a + b) (a-b) detailed solution process
=a²－2ab－b-a²+b²
=b²－2ab－b
=b(b-2a-1)
Original formula = a ^ 2-2ab-b - (a ^ 2-B ^ 2)
=b^2-2ab-b
=b(b-2a-1)
Original formula = a ^ 2-2ab-b - (a ^ 2-B ^ 2)
=b^2-2ab-b
=b(b-2a-1)
It is known that the shape of the square of the parabola y = a (x + m) is the same as the square of y equal to 3x, and the axis of symmetry is a straight line, X equal to 3. The analytical formula of this parabola is obtained
emergency
The shape of the square of the parabola y = a (x + m) is the same as that of y equal to 3x
So the corresponding coefficients of x ^ 2 are equal
y=a(x+m)^2=ax^2+2amx+am^2
So a = 3
The axis of symmetry is a straight line, x equals 3,
So - 2am / 2A = 3, M = - 3
So the analytic formula of object line is 3x ^ 2-18x + 27