Answer:
(x-1) is a factor of the polynomial.
Step-by-step explanation:
Given:
f(x) = x³ + 6x² + 3x - 10
It is required to find which option is a factor of the given polynomial.
Factor the term (-10):
-10 = 1 * -10
= -1 * 10
= 2 * -5
= -2 * 5
As the given options are: (x+1) , (x-1) , (x-2) , (x-10)
So, the possible roots are: -1 , 1 , 2 , 10
So,
we will Check the values -1 , 1 , 2 , 10 to find which of them will make f(x)= 0
If x = -1 ⇒ f(x) = (-1)³ + 6*(-1)² + 3*(-1) - 10 = -1 + 6 - 3 - 10 = -8
So, x = -1 is not one of the roots ⇒ (x-1) is not one of the factor.
If x = 1 ⇒ f(x) = 1³ + 6*1² + 3*1 - 10 = 1 + 6 + 3 - 10 = 0
So, x = 1 is one of the roots ⇒ (x-1) is one of the factor
The other values { 2 , 10} also are not the roots of the function
So, the answer is the second option
(x-1) is a factor of the polynomial.
