Question

Factorise the following:

x⁴ + 2x³ + 3x² + 6x

Answer 1

Given: x⁴ + 2x³ + 3x² + 6x

Step-wise calculation:

1. First, take out the common factor (x):

x(x³ + 2x² + 3x + 6)

2. Now, factor the cubic polynomial inside the bracket (x³ + 2x² + 3x + 6).

We can try factoring by grouping:

Group terms as:

(x³ + 2x²) + (3x + 6)

Take common factors from each group:

x²(x + 2) + 3(x + 2)

3. Now factor out the common binomial factor (x + 2):

(x + 2)(x² + 3)

The fully factorized form is x(x + 2)(x² + 3).