There is a factor of 2x ^ 3 - x ^ 2 + m, which is 2x + 1 What is the undetermined coefficient method? I haven't learned it. Is there a simpler one?

There is a factor of 2x ^ 3 - x ^ 2 + m, which is 2x + 1 What is the undetermined coefficient method? I haven't learned it. Is there a simpler one?

By undetermined coefficient method
Let 2x ^ 3-x ^ 2 + M = (2x + 1) (x ^ 2 + BX + C)
=2x^3+(2b+1)x^2+(b+2c)x+c
So we have 2B + 1 = - 1, B + 2C = 0, C = M
So m = 1 / 2

The factorization factor of 2x ^ 3 + 2x ^ 2-12x + K has a factor (2x + 1) to find the value of K

2x^3+2x^2-12x+k
= (2x^3+x^2) + (x^2+1/2x ) - (25/2x-k)
= x^2(2x+1) + 1/2x(2x+1) - 25/4[2x+(-4/25k)]
2X ^ 3 + 2x ^ 2-12x + K factorization has a factor (2x + 1)
(-4/25k) = 1
k = -25/4

A factor of the fourth power of X + the third power of 2x - x + m is (x + 1), and the value of M is obtained

4 times of X + 3 times of 2x - x + M
=x³（x+1）+x³-x+m
=x³（x+1）+x(x+1)(x-1)+m
m=0
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