Question

Is x + 1 a factor of 6x^3+7x^2
- x - 27?

Answer 1

Step-by-step explanation:

$the \: zero \: of \: x + 1 \: is - 1$

$let \: p(x) \: = {6}x^{3} + 7 {x}^{2} - x - 27$

$p( - 1) = 6 \times ( - 1) {}^{3} + 7 \times { - 1}^{2} - ( - 1) - 27$

$p( - 1) = 6 \times ( - 1) + 7 \times 1 - ( - 1) - 27$

$p( - 1) = - 6 + 7 + 1 - 27$

$p( - 1) = - 33 + 8$

$p( - 1) = - 25$

So, by factor theorem, x+1 is not a factor of 6x^3+7x^2-x-27.