Question

2x² + x - 3 which of the expressions below matches with the equation above? (graph it and check it or multiply binomial factors using box method!) (2x - 3)(x + 1) (2x + 3)(x - 1) (3x - 1)(x - 2) (2x + 3)(x + 4)

Explanation:

Step1: Expand option A

$$\begin{align*} (2x - 3)(x + 1) &= 2x\cdot x + 2x\cdot1 - 3\cdot x - 3\cdot1\\ &=2x^2 + 2x - 3x - 3\\ &=2x^2 - x - 3 \end{align*}$$

Step2: Expand option B

$$\begin{align*} (2x + 3)(x - 1) &= 2x\cdot x + 2x\cdot(-1) + 3\cdot x + 3\cdot(-1)\\ &=2x^2 - 2x + 3x - 3\\ &=2x^2 + x - 3 \end{align*}$$

Step3: Verify match

The result of Step2 matches the given expression.

Answer:

B. $(2x + 3)(x - 1)$