Question

Factors of (3 – x – 4x²) are ______.

Options

• (4x + 3) (1 – х)

• (3 – 4x) (1 + x)

• (4x + 3) (1 + x)

• (3 – 4x) (1 – x)

Answer 1

Factors of (3 – x – 4x²) are (3 – 4x) (1 + x).

Explanation: 

We are given the expression: 3 – x – 4x² 

Let's rearrange it in standard form: –4x² – x + 3

Now factor it.

Step 1: Multiply the coefficient of x² and the constant:

–4 × 3 = –12

We need two numbers that multiply to –12 and add up to –1 the coefficient of x:

These numbers are –4 and 3.

Step 2: Split the middle term:

–4x² – 4x + 3x + 3

= (–4x² – 4x) + (3x + 3)

= –4x(x + 1) + 3(x + 1)

= (x + 1)(–4x + 3)

So, 3 – x – 4x² = (3 – 4x)(1 + x).