Question 1Structured · 3 marksA* challenge
The cubic equation x3 − 7x − 6 = 0 has a root x = −2.
Find the other two roots.
Show answers and mark scheme
| Part | Answer and marking points | Marks |
|---|---|---|
| −1, 3 divide by (x + 2) M1 quadratic factor A1 −1, 3 A1 | 3 |
Free Factors of polynomials questions for IGCSE Additional Mathematics (0606), part of Algebra. Each question has the answer and the marking points an examiner would look for.
Generate a full Factors of Polynomials worksheet →All Algebra questionsThe cubic equation x3 − 7x − 6 = 0 has a root x = −2.
Find the other two roots.
| Part | Answer and marking points | Marks |
|---|---|---|
| −1, 3 divide by (x + 2) M1 quadratic factor A1 −1, 3 A1 | 3 |
p(x) = 2x3 + x2 + 4x + 5
Find the remainder when p(x) is divided by (x − 3).
| Part | Answer and marking points | Marks |
|---|---|---|
| 80 p(3) M1 80 A1 | 2 |
p(x) = x3 + ax2 + bx − 16
It is given that x − 2 is a factor of p(x) and that when p(x) is divided by x + 1 the remainder is −9.
Find the values of a and b.
Factorise p(x) completely.
Hence solve p(x) = 0.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | a = 4, b = −4 p(2) = 0 used M1 p(−1) = −9 used M1 Solve simultaneously M1 a = 4, b = −4 A1 | 4 |
| (b) | (x − 2)(x + 2)(x + 4) Quadratic factor found M1 Complete factorisation A1 | 2 |
| (c) | 2, −2, −4 2, −2, −4 B1 | 1 |
The cubic equation x3 + 3x2 − x − 3 = 0 has a root x = −1.
Find the other two roots.
| Part | Answer and marking points | Marks |
|---|---|---|
| −3, 1 divide by (x + 1) M1 quadratic factor A1 −3, 1 A1 | 3 |
p(x) = 2x3 + x2 + x + 2
Find the remainder when p(x) is divided by (x + 1).
| Part | Answer and marking points | Marks |
|---|---|---|
| 0 p(−1) M1 0 A1 | 2 |
p(x) = x3 + ax2 + bx + 12
It is given that x − 4 is a factor of p(x) and that when p(x) is divided by x + 2 the remainder is 18.
Find the values of a and b.
Factorise p(x) completely.
Hence solve p(x) = 0.
| Part | Answer and marking points | Marks |
|---|---|---|
| (a) | a = −2, b = −11 p(4) = 0 used M1 p(−2) = 18 used M1 Solve simultaneously M1 a = −2, b = −11 A1 | 4 |
| (b) | (x − 4)(x + 3)(x − 1) Quadratic factor found M1 Complete factorisation A1 | 2 |
| (c) | 4, −3, 1 4, −3, 1 B1 | 1 |
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