Use the factor theorem to determine whether gx is factor of fx in each

1.	Use the factor theorem to determine whether gx is factor of fx in each of the following cases fx 5 x cube + x square -5 x -1 gx is equals to X + 1
Answer» Given : A POLYNOMIAL 5x³ + x² - 5X -1 . To Find : Whether X +1 is a FACTOR of given polynomial or not . Solution : $\longmapsto\tt{x+1=0}$ $\longmapsto\tt\bf{x=-1}$ Putting x = -1 : $\longmapsto\tt{{5x}^{3}+{x}^{2}-5x-1}$ $\longmapsto\tt{5{(-1)}^{3}+{(-1)}^{2}-5(-1)-1}$ $\longmapsto\tt{5(-1)+1+5-1}$ $\longmapsto\tt{-5+1+5-1}$ $\longmapsto\tt{-4+4}$ $\longmapsto\tt\bf{0}$ So , x + 1 is the factor of 5x³ + x² - 5x - 1 ...