I don't know if i did this correctly
is(x-1) a factor of 17x^10+16x^6+1
its no.. right?
To determine if (x-1) is a factor of the polynomial 17x^10 + 16x^6 + 1, we can use the Remainder Theorem.
The Remainder Theorem states that if a polynomial f(x) is divided by (x - a), the remainder is equal to f(a).
In this case, (x-1) is the divisor, and we want to check if the remainder is zero when we divide the polynomial by (x-1).
We can evaluate the polynomial at x = 1:
f(1) = 17(1)^10 + 16(1)^6 + 1
= 17 + 16 + 1
= 34.
Since the remainder is not zero (it is 34), (x-1) is not a factor of the polynomial 17x^10 + 16x^6 + 1.
In this scenario, you did it correctly by evaluating the polynomial at x=1 to check if (x-1) is a factor. Since the remainder is not zero, it means (x-1) is not a factor of the polynomial.