Answer:
we can conclude that x-1 is not a factor of p(x) = [tex]-2x^{4} + x^{3} - 4x +7[/tex].
Step-by-step explanation:
To determine whether x-1 is a factor of p(x) = [tex]-2x^{4} + x^{3} - 4x +7[/tex] , we can use the factor theorem.
The factor theorem states that if a polynomial p(x) has a factor of the form (x - k), then p(k) = 0.
In this case, we need to evaluate p(x) at x = 1 to check if p(1) equals zero.
p(1) = -2(1)^4 + (1)^3 - 4(1) + 7
= -2 + 1 - 4 + 7
= 2
Since p(1) is not equal to zero, x-1 is not a factor of p(x).
Therefore, we can conclude that x-1 is not a factor of p(x) = [tex]-2x^{4} + x^{3} - 4x +7[/tex].
