Question
Factorise:
x3 - 3x2 + 3x + 7
x3 - 3x2 + 3x + 7
✓
Answer
x3 - 3x2 + 3x + 7
= x3 - 3x2 + 3x - 1 + 8
= (x3 - 3x2 + 3x - 1) + 8
= (x - 1)3 + 23
= (x - 1 + 2)[(x - 1)2 - (x - 1)(2) + 22]
= (x + 1)(x2 - 2x + 1 - 2x + 2 + 4)
= (x + 1)(x2 - 4x + 7)
= x3 - 3x2 + 3x - 1 + 8
= (x3 - 3x2 + 3x - 1) + 8
= (x - 1)3 + 23
= (x - 1 + 2)[(x - 1)2 - (x - 1)(2) + 22]
= (x + 1)(x2 - 2x + 1 - 2x + 2 + 4)
= (x + 1)(x2 - 4x + 7)
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
Factorise:
x2 - (a + b)x + ab
x2 - (a + b)x + ab
Which of the following figures lie on the same base and between the same parallels. In such a case, write the common base and two parallels:
Write the reciprocal $5+\sqrt2.$
→Classify the number 7.478478..... as rational or irrational.
Factorise:
2x4 - 32
2x4 - 32
Find the ratio of the total surface area and lateral surface area of a cube.
Solve the following equations for x:
$2^{\text{x}+1}=4^{\text{x}-3}$
→$2^{\text{x}+1}=4^{\text{x}-3}$
Retionalise the denominator of each of the following:
$\frac{\sqrt3+1}{2}$
→$\frac{\sqrt3+1}{2}$
ABC and DBC are two isosceles triangles on the same base BC. Show that ∠ABD = ∠ACD.
D and E are points on sides AB and AC respectively of $\triangle\text{ABC}$ such that$\text{ar}(\triangle\text{BCD})=\text{ar}(\triangle\text{BCE}).$ Prove that DE || BC.
→