Algebra: Dividing Polynomials

Difficult

Q1) Divide $x ^{3} + 12 x ^{2} + 45 x + 54$ by $x+ 6$
Q1) Show that +3 is a factor $x ^{3} - 4 x ^{2} - 9 x + 36$
Q1) Given that -3 is a factor $x ^{3} + 7 x ^{2} - 9 x - 63$ fully factorise $x ^{3} + 7 x ^{2} - 9 x - 63$
Q2) Divide $x ^{3} + 8 x ^{2} - 44 x - 240$ by $x+ 10$
Q2) Show that -5 is a factor $x ^{3} + 5 x ^{2} - 4 x - 20$
Q2) Given that -3 is a factor $x ^{3} + 14 x ^{2} + 63 x + 90$ fully factorise $x ^{3} + 14 x ^{2} + 63 x + 90$
Q3) Divide $x ^{3} + 14 x ^{2} + 28 x - 120$ by $x+ 6$
Q3) Show that +6 is a factor $x ^{3} - 7 x ^{2} - 6 x + 72$
Q3) Given that +2 is a factor $x ^{3} + 11x ^{2} + 14 x - 80$ fully factorise $x ^{3} + 11x ^{2} + 14 x - 80$
Q4) Divide $x ^{3} + 4 x ^{2} - 25 x - 28$ by $x+ 7$
Q4) Show that -5 is a factor $x ^{3} + 8 x ^{2} + 17 x + 10$
Q4) Given that -2 is a factor $x ^{3} + 14 x ^{2} + 51x + 54$ fully factorise $x ^{3} + 14 x ^{2} + 51x + 54$
Q5) Divide $x ^{3} + 17 x ^{2} + 82 x + 120$ by $x+ 3$
Q5) Show that +2 is a factor $x ^{3} - x ^{2} - 32 x + 60$
Q5) Given that +4 is a factor $x ^{3} - 5 x ^{2} - 16 x + 80$ fully factorise $x ^{3} - 5 x ^{2} - 16 x + 80$