Question

check if X + 1 is a factor of p(X) = x³ - x² - (2+✓2) X -✓ 2​

Answer 1

Answer:

x + 1 is not a factor of p(x) .

Step-by-step explanation:

Let x + 1 = 0 => x = -1

$p(x) = {x}^{3} - {x}^{2} - (2 + \sqrt{2})x - \sqrt{2} \\ p( - 1) = ( { - 1})^{3} - ( { - 1})^{2} - (2 + \sqrt{2} )( - 1) - \sqrt{2} \\ = - 1 - 1 \: + 2 \: - \sqrt{2} - \sqrt{2} \\ = - 2 \: + \: 2 \: - \: 2 \sqrt{2} \\ = 0 \: - \: 2 \sqrt{2} \\ = 2 \sqrt{2}$

As p(-1) is not equal to 0 , so x + 1 is not a factor of p(x) .