the question:-

Consider the polynomial p(x)=5x^39x^227x5.

a) The equation p(x)=0 has a rational root. Find this by applying theorem 7 in the course literature.

b) Use polynomial division and square completion to find the other roots of p(x). For polynomial division, you do not need to show all the steps, it is enough to enter the quotient and remainder.

c) Factorize p(x), that is, write p(x) as a product of polynomials of degree 1.Your solution must be well written and your conclusion clearly formulated. Explain reasoning using both text and mathematical symbols. Only calculations are not accepted.All theorems in the course literature may be used without proof.

my answer:-

Since x=...... is a root, (x+ 15) is a factor of p(x).If we divide p(x) by (x+ 15) we get-----We will factor......It will be impossible to split the midterm here,so we use the formula x = ....

Other roots of p

b) Eftersom x=x= = 5 ar en rot sa ar (x+ ~) en faktor av p(x). Om vi dividerar p(x) med (x+ = ) sa kommer vi fa 5plox 272 5 -5/2 -10x-25 Vi kommer att faktorisera 5x2 - 10x - 25=0 Det blir omojligt att dela upp mellantermen har, sa vi anvander oss av formeln x = - bev/b' dac 2a (-10)+/(-10)"-4(5)(-25) =>X= 2(5) (10) 4 10,/6 => X= (10) =(1+ 6) Andra rotter av p(x) , x= (1 + v6), (1 - v6)C) p(x) = 5x3 - 9x2 - 27x - 5 p(x) = 5:13 - 912 - 27x - 5 =(x + =)(5x2 - 10x - 25) =C+ )(x+v6-1)(x -V6-1) p(x) = (x+ !)(x -1+ V6)(x -1 -V6)