Check wheter 7+3x is a factor of 3x cube + 7x
Answers
step:1
step:1put divider =0
step:1put divider =07+3x=0
step:1put divider =07+3x=0 3x=-7
step:1put divider =07+3x=0 3x=-7x-7/3
step:1put divider =07+3x=0 3x=-7x-7/3step :2
step:1put divider =07+3x=0 3x=-7x-7/3step :2let = p(x) =3x^3 +7x
step:1put divider =07+3x=0 3x=-7x-7/3step :2let = p(x) =3x^3 +7xputting x=-7/3
step:1put divider =07+3x=0 3x=-7x-7/3step :2let = p(x) =3x^3 +7xputting x=-7/3p(-7/3) =3 (-7^3/3) +7(-7/3)0
step:1put divider =07+3x=0 3x=-7x-7/3step :2let = p(x) =3x^3 +7xputting x=-7/3p(-7/3) =3 (-7^3/3) +7(-7/3)0=-3(7^3 /3^3)-49/3
step:1put divider =07+3x=0 3x=-7x-7/3step :2let = p(x) =3x^3 +7xputting x=-7/3p(-7/3) =3 (-7^3/3) +7(-7/3)0=-3(7^3 /3^3)-49/3 =343/9 - 49/3
step:1put divider =07+3x=0 3x=-7x-7/3step :2let = p(x) =3x^3 +7xputting x=-7/3p(-7/3) =3 (-7^3/3) +7(-7/3)0=-3(7^3 /3^3)-49/3 =343/9 - 49/3 =-343-49(3) / 9
step:1put divider =07+3x=0 3x=-7x-7/3step :2let = p(x) =3x^3 +7xputting x=-7/3p(-7/3) =3 (-7^3/3) +7(-7/3)0=-3(7^3 /3^3)-49/3 =343/9 - 49/3 =-343-49(3) / 9 = -343-147/9
step:1put divider =07+3x=0 3x=-7x-7/3step :2let = p(x) =3x^3 +7xputting x=-7/3p(-7/3) =3 (-7^3/3) +7(-7/3)0=-3(7^3 /3^3)-49/3 =343/9 - 49/3 =-343-49(3) / 9 = -343-147/9 =-590/9
step:1put divider =07+3x=0 3x=-7x-7/3step :2let = p(x) =3x^3 +7xputting x=-7/3p(-7/3) =3 (-7^3/3) +7(-7/3)0=-3(7^3 /3^3)-49/3 =343/9 - 49/3 =-343-49(3) / 9 = -343-147/9 =-590/9the remainder =p(-7/3) =-590/9
step:1put divider =07+3x=0 3x=-7x-7/3step :2let = p(x) =3x^3 +7xputting x=-7/3p(-7/3) =3 (-7^3/3) +7(-7/3)0=-3(7^3 /3^3)-49/3 =343/9 - 49/3 =-343-49(3) / 9 = -343-147/9 =-590/9the remainder =p(-7/3) =-590/9since remainder is not 0
step:1put divider =07+3x=0 3x=-7x-7/3step :2let = p(x) =3x^3 +7xputting x=-7/3p(-7/3) =3 (-7^3/3) +7(-7/3)0=-3(7^3 /3^3)-49/3 =343/9 - 49/3 =-343-49(3) / 9 = -343-147/9 =-590/9the remainder =p(-7/3) =-590/9since remainder is not 0thus 7+3x is not factor of3x^3+7x.