Question

x² – 10x + 24 is equal to ______.

Options

• (x – 6) (x – 4)

• (x – 12) (x + 2)

• (x + 6) (x – 4)

• (x + 12) (x – 2)

Answer 1

x² – 10x + 24 is equal to (x – 6) (x – 4).

Explanation:

To factorise x² – 10x + 24, we need to find two numbers that multiply to 24 and add up to –10.

Step 1: Find the factors of 24 that add up to –10.

The factors of 24 are:

1 × 24,

–1 × –24,

2 × 12,

–2 × –12,

3 × 8,

–3 × –8,

4 × 6,

–4 × –6

We see that –4 and –6 multiply to give 24 and add up to −10.

Step 2: Factor the quadratic.

Now, we can rewrite x² – 10x + 24 as:

x² – 4x – 6x + 24

Group the terms:

(x² – 4x) – (6x – 24)

Factor each group:

x(x – 4) – 6(x – 4)

Now factor out the common binomial factor (x – 4):

(x – 4) (x – 6)

Final factorisation:

Thus, the factorisation is (x – 6) (x – 4)