Final answer:
To identify which binomial is a factor of x´ - 4x² - 4x + 8, we can substitute the x value from each option into the polynomial and look for which one yields a result of zero.
Step-by-step explanation:
The student is asking which binomial is a factor of the polynomial x´ - 4x² - 4x + 8. To find out which of the options given is a factor, we can use the fact that if a binomial (x - r) is a factor of a polynomial, then r is a root of the polynomial equation set to zero. Hence, plugging these values into the polynomial should yield zero. We have to check each binomial by substituting the x value from the binomial into the original polynomial.
- For option A (x - 2), we substitute x = 2 into the polynomial and calculate:
- For option B (x + 2), we substitute x = -2 into the polynomial and calculate:
- For option C (x - 4), we substitute x = 4 into the polynomial and calculate:
- For option D (x + 4), we substitute x = -4 into the polynomial and calculate:
By performing these calculations, we can determine which binomial, when substituted into the polynomial, gives a result of zero, indicating it is a factor of the polynomial in question.