Question

2x² – x – 15 is equal to ______.

Options

• (2x – 3) (x + 5)

• (2x + 3) (x – 5)

• (x – 3) (2x + 5)

• (x + 3) (2x – 5)

Answer 1

2x² – x – 15 is equal to (x – 3) (2x + 5).

Explanation:

We are given the quadratic expression 2x² – x – 15. We need to factorise it.

Step 1: Multiply the coefficient of x² (which is 2) and the constant term (which is –15):

2 × (–15) = –30

Step 2: Find two numbers that multiply to –30 and add up to the coefficient of x (which is –1).

The two numbers that multiply to –30 and add up to –1 are 5 and –6, since:

5 × (–6) = –30 and 5 + (–6) = –1

Step 3: Rewrite the middle term –x using these two numbers:

2x² + 5x – 6x – 15

Step 4: Group the terms:

(2x² + 5x) – (6x + 15)

Step 5: Factor each group:

x(2x + 5) – 3(2x + 5)

Step 6: Factor out the common binomial factor (2x + 5):

(2x + 5) (x – 3)

Final factorisation:

Thus, the factorisation is (2x + 5) (x – 3)