Question

Check whether x+1 is a factor of 5x³+x²-5x-1 using factor theorem.​

Answer 1

Answer:

5x³+x²-5x-1.

x+1=0.

x=-1.

5(-1)³+(-1)²-5(-1)-1.

5(-1)+(1)+5-1. (Because -×-=+).

-5+1+5-1. (Because +×-=-).

0. (Because +×-=- & -×+=- so, -5+5 & +1-1 will cancel).

I think this is your answer.

Answer 2

Answer:

Step-by-step explanation:

Factor Theorem :

Let p(x) be a polynomial if  degree one or more than one   and a is a real number .Then ,

i ) x - a , will be a factor of p(x)

if p(a) = 0 conversely

ii ) If x - a is a factor of p(x),

Then p(a) = 0

Here ,

F(x) = 5x³ + x² - 5x - 1 ,

g(x) = x + 1 ,

g(x) = 0 ,

=> x + 1 = 0

=> x = -1

Therefore ,

Zero of g(x) is -1 ,

Now ,

F(-1) = 5(-1)³ + (-1)² - 5(-1) - 1

= -5 + 1 + 5 - 1

=-6 + 6

= 0

Therefore ,  

By Factor theorem ,

g(x) is a factor of F(x)