If `x-c` is a factor of order `m` of the polynomial `f(x)` of degree `n(1

x+1 is a factor of the polynomial

(x+1) is a factor of the polynomial

(x+1) is a factor of the polynomial

Assertion : (x+2) and (x-1) are factors of the polynomial x^(4)+x^(3)+2x^(2)+4x-8 . Reason : For a polynomial p(x) of degree ge1, x-a is a factor of the polynomial p(x) if and only if p(a)ge1 .

If x-r is a factor of the polynomial f(x)=a_(0)x^(n)+a_(1)x^(n-1)+...+a_(n) repeated m xx,(1

For a polynomial p(x) of degree ge1, p(a)=0 , where a is a real number, then (x-a) is a factor of the polynomial p(x) Find the value of k if x-1 is a factor of 4x^(3)+3x^(2)-4x+k .

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

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