If `x-c` is a factor of order `m` of the polynomial `f(x)` of degree n (1 < m < n) , then find the polynomials for which `x=c` is a root.

x+1 is a factor of the polynomial

If x+1 is a factor of the polynomial 2x^(2)+kx, then the value of k is

If x-r is a factor of the polynomial f(x)=a_0x^n+a_1x^(n-1)+.....+a_n repeated m times, (1ltxlt=n), then r is a root of f^(prime)(x)=0 repeated m times.True/False.

If (x-1) is a factor of polynomial f(x) but not of g(x) , then it must be a factor of (a) f(x)g(x) (b) -f\ (x)+\ g(x) (c) f(x)-g(x) (d) {f(x)+g(x)}g(x)

If n be a natural number define polynomial f_(n)(x) of n^(th) degree as follows f_(n)(costheta)cosntheta i.e. f_(2)(x)=2x^(2)-1 f_(3)(x)=4x^(3)-3x_(1) Then f_(6)(x) is equal to

If a is defined by f (x)=a_(0)x^(n)+a_(1)x^(n-2)+a_(2)x^(n-2)+...+a_(n-1)x+a_(n) where n is a non negative integer and a_(0),a_(1),a_(2),…….,a_(n) are real numbers and a_(0) ne 0, then f is called a polynomial function of degree n. For polynomials we can define the following theorem (i) Remainder theorem: Let p(x) be any polynomial of degree greater than or equal to one and 'a' be a real number. if p(x) is divided by (x-a), then the remainder is equal to p(a). (ii) Factor theorem : Let p(x) be a polynomial of degree greater than or equal to 1 and 'a' be a real number such that p(a) = 0, then (x-a) is a factor of p(x). Conversely, if (x-a) is a factor of p(x). then p(a)=0. The factor of the polynomial x^(3)+3x^(2)+4x+12 is (1) x+3" "(2) x-3" "(3) x+2" "(4) x-2

If n be a natural number define polynomial f_(n)(x) of n^(th) degree as follows f_(n)(costheta)cosntheta i.e. f_(2)(x)=2x^(2)-1 f_(3)(x)=4x^(3)-3x_(1) Then (x+sqrt(x^(2)-1))^(10)+(x-sqrt(x^(2)-1s))^(10) is equal to

Show that (x-2) is a factor of the polynomial f(x)=2x^3-3x^2-17 x+30 and hence factorize f(x)dot

Show that (x-2) is a factor of the polynomial f(x)=2x^3-3x^2-17 x+30 and hence factorize f(x)dot