Question

3x² + 2x – 8 is equal to ______.

पर्याय

• (3x + 4) (x – 2)

• (3x – 4) (x + 2)

• (3x – 8) (x + 1)

• (3x + 8) (x – 1)

Answer 1

3x² + 2x – 8 is equal to (3x – 4) (x + 2).

Explanation:

Let’s factorize the expression 3x² + 2x – 8

Step 1: Multiply the coefficient of x² (which is 3) and the constant term (which is –8):

3 × (–8) = –24

Step 2: Find two numbers that multiply to –24 and add up to the coefficient of x (which is 2).

The two numbers that multiply to –24 and add up to 2 are 6 and –4, since:

6 × (–4) = –24 and 6 + (–4) = 2

Step 3: Rewrite the middle term 2x using 6x and –4x:

3x² + 6x – 4x – 8

Step 4: Group the terms:

(3x² + 6x) – (4x + 8)

Step 5: Factor each group:

3x(x + 2) – 4(x + 2)

Step 6: Factor out the common binomial factor (x + 2):

(3x – 4) (x + 2)

Final factorisation:

Thus, the factorisation is (3x – 4) (x + 2).