Algebra: Dividing Polynomials

Easy

Medium

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 \(x ^{3} - 5 x ^{2} - 16 x + 80 \)