Algebra: Dividing Polynomials

Easy

Medium

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 \( x ^{3} + x ^{2} - 22 x - 40 \)