Question

check whether ( x-1) is a factor of 4 x³+ 5 x² - 3x + 6

Answer 1

let p (x) = 4x^3 +5x^2 -3x +6
using factor theorem
x=1
now, after putting the value of x in polynomial p (x)

p (1)= 4 (1)^3 +5 (1)^2-3 (1)+6
= 4 +5-3+6
= 12
As we can see that the remainder isn't equal to 0
so, by factor theorem (x-1) isn't a factor of polynomial p (x).