Question

when written in factored form, $4w^2 - 11w - 3$ is equivalent to

1. $(2w + 1)(2w - 3)$
2. $(2w - 1)(2w + 3)$
3. $(4w + 1)(w - 3)$
4. $(4w - 1)(w + 3)$

Explanation:

Step1: Expand Option 1

Multiply \((2w + 1)(2w - 3)\) using FOIL: \(2w\times2w + 2w\times(-3)+1\times2w + 1\times(-3)=4w^2-6w + 2w-3 = 4w^2-4w - 3\). Not equal to \(4w^2-11w - 3\).

Step2: Expand Option 2

Multiply \((2w - 1)(2w + 3)\) using FOIL: \(2w\times2w+2w\times3+(-1)\times2w+(-1)\times3 = 4w^2+6w-2w - 3=4w^2 + 4w-3\). Not equal to \(4w^2-11w - 3\).

Step3: Expand Option 3

Multiply \((4w + 1)(w - 3)\) using FOIL: \(4w\times w+4w\times(-3)+1\times w+1\times(-3)=4w^2-12w+w - 3=4w^2-11w - 3\). This matches the original quadratic.

Step4: Expand Option 4 (for completeness)

Multiply \((4w - 1)(w + 3)\) using FOIL: \(4w\times w+4w\times3+(-1)\times w+(-1)\times3=4w^2+12w - w-3=4w^2+11w - 3\). Not equal to \(4w^2-11w - 3\).

Answer:

1. \((4w + 1)(w - 3)\)