Question

x² – 5x + 6 is equal to ______.

विकल्प

• (x + 2) (x + 3)

• (x – 6) (x + 1)

• (x – 1) (x + 6)

• (x – 2) (x – 3)

Answer 1

x² – 5x + 6 is equal to (x – 2) (x – 3).

Explanation:

To factorise x² – 5x + 6, we need to find two numbers that multiply to 6 and add up to –5.

Step 1: Find the factors of 6 that add up to −5.

The factors of 6 are:

1 × 6,

–1 × –6,

2 × 3,

–2 × –3

We see that –2 and –3 multiply to give 6 and add up to –5.

Step 2: Factor the quadratic.

Now, we can rewrite x² – 5x + 6 as:

x² – 2x – 3x + 6

Group the terms:

(x² – 2x) – (3x – 6)

Factor each group:

x(x – 2) – 3(x – 2)

Now factor out the common binomial factor (x – 2):

(x – 2) (x – 3)

Final factorisation:

Thus, the factorisation is (x – 2) (x – 3)