Question

x² – 8x + 12 is equal to ______.

विकल्प

• (x – 4) (x – 3)

• (x – 6) (x + 2)

• (x + 4) (x + 3)

• (x – 6) (x – 2)

Answer 1

x² – 8x + 12 is equal to (x – 6) (x – 2).

Explanation:

We are given the quadratic expression x² – 8x + 12. Let’s factorise it.

Step 1: Find two numbers that multiply to 12 (the constant term) and add up to –8 (the coefficient of x).

The factors of 12 are:

1 × 12,

–1 × –12,

2 × 6,

–2 × –6,

3 × 4,

–3 × –4

We see that –6 and –2 multiply to give 12 and add up to –8.

Step 2: Rewrite the middle term –8x using –6 and –2:

x² – 6x – 2x + 12

Step 3: Group the terms:

(x² – 6x) – (2x – 12)

Step 4: Factor each group:

x(x – 6) – 2(x – 6)

Step 5: Factor out the common binomial factor (x – 6):

(x – 6) (x – 2)

Final factorisation:

Thus, the factorisation is (x – 6) (x – 2).