Algebra: Dividing Polynomials

## Difficult

Q1) Divide $x ^{3} + 10 x ^{2} - 36 x - 360$ by $x+ 6$
Q1) Show that +5 is a factor $x ^{3} - 7 x ^{2} - 14 x + 120$
Q1) Given that -6 is a factor $x ^{3} + 5 x ^{2} - 8 x - 12$ fully factorise $x ^{3} + 5 x ^{2} - 8 x - 12$
Q2) Divide $x ^{3} + 21x ^{2} + 146 x + 336$ by $x+ 7$
Q2) Show that -6 is a factor $x ^{3} + 19 x ^{2} + 120 x + 252$
Q2) Given that -2 is a factor $x ^{3} + 13 x ^{2} + 46 x + 48$ fully factorise $x ^{3} + 13 x ^{2} + 46 x + 48$
Q3) Divide $x ^{3} + 12 x ^{2} + 44 x + 48$ by $x+ 2$
Q3) Show that -5 is a factor $x ^{3} + 19 x ^{2} + 115 x + 225$
Q3) Given that -3 is a factor $x ^{3} + 11x ^{2} + 39 x + 45$ fully factorise $x ^{3} + 11x ^{2} + 39 x + 45$
Q4) Divide $x ^{3} + 9 x ^{2} - 21x - 245$ by $x+ 7$
Q4) Show that +5 is a factor $x ^{3} - x ^{2} - 41x + 105$
Q4) Given that +4 is a factor $x ^{3} + 7 x ^{2} - 16 x - 112$ fully factorise $x ^{3} + 7 x ^{2} - 16 x - 112$
Q5) Divide $x ^{3} + 18 x ^{2} + 92 x + 120$ by $x+ 10$
Q5) Show that +2 is a factor $x ^{3} - 2 x ^{2} - 9 x + 18$
Q5) Given that -4 is a factor $x ^{3} + x ^{2} - 22 x - 40$ fully factorise $x ^{3} + x ^{2} - 22 x - 40$