Question

verify division algorithm for the polynomial f (x)=8+20x+x square -6x cube and g (x)=2+5x-3x square.

Answer 1

The division ofthe polynomial 3x4-5x3-10x2-20x-8 by the polynomial 3x2-5x+2using long division: x2-4 3x2-5x+2 3x4-5x3-10x2-20x-8 3x4-5x3+2x2 -12x2-20x-8 -12x2-20x-8 0 So, by long division methhod the quotient is x2-4 and the remainder is 0.Hence, by division algorithm, we havepx=gx×qx+rx⇒ 3x4-5x3-10x2-20x-8 =3x2-5x+2x2-4+0As, the remainder is zero, therefore by factor theorem 3x2-5x+2 of 3x4-5x3-10x2-20x-8.

Answer 2

it is given that -1 is one of the zeros of the polynomial x cube +2x square -11x-12. Find all it is given that -1 is one of the zeros of the polynomial x cube +2x square -11x-12. Find all the zeros of the given polynomial. zeros of the given polynomial.