Find the number of polynomials of the form `x^3+a x^2+b x+c` that are divisible by `x^2+1,w h e r ea , b ,c in {1,2,3,9,10}dot`

The number of polynomials of the form x^(3)+ax^(2)+bx+c that are divisible by x^(2)+1 , where a, b,c in{1,2,3,4,5,6,7,8,9,10} , is

If the polynomial 7x^(3)+ax+b is divisible by x^(2)-x+1 , find the value of 2a+b.

Find the values of a and b so that the polynomial x^(3)+10x^(2)+ax+b is exactly divisible by x-1 as well as x-2 .

Find the value of a and b so that the polynomial x^(3)+10x^(2)+ax+b is exactly divisible by (x-1) and (x-2).

Find the values of a and b so that the polynomial (x^(3)-10x^(2)+ax+b) is exactly divisible by (x -1) as well as (x -2).

True or false The equation 2x^2+3x+1=0 has an irrational root. If a

Find the values of a and b so that the polynomial (x^(3)-10x^(2)+ax+b) is exactly divisible by (x-1) as well as (x-2) .

Given that the zeros of the cubic polynomial f(x) = x^3 -6 x^2 + 3x + 10 are a, a+b, a + 2b for some real number a and b. Find the values of a and b as well as the zeros of the given polynomial.