Question

x² – 15x – 54 is equal to ______.

पर्याय

• (x – 9) (x – 6)

• (x – 9) (x + 6)

• (x – 18) (x + 3)

• (x + 18) (x – 3)

Answer 1

x² – 15x – 54 is equal to (x – 18) (x + 3).

Explanation:

To factorise x² – 15x – 54, we need to find two numbers that multiply to –54 and add up to –15.

Step 1: Find the factors of –54 that add up to –15.

The factors of –54 are:

–1 × 54,

1 × –54,

–2 × 27,

2 × –27,

–3 × 18,

3 × –18,

–6 × 9,

6 × –9

We see that –18 and 3 multiply to give –54 and add up to –15.

Step 2: Factor the quadratic.

Now, we can write x² – 15x – 54 as:

x² – 18x + 3x – 54

Group the terms:

(x² – 18x) + (3x – 54)

Factor each group:

x(x – 18) + 3(x – 18)

Now factor out the common binomial factor (x – 18):

(x – 18) (x + 3)

Final factorisation:

Thus, the factorisation is (x – 18) (x + 3)