Chapter 8.6, Problem 2STP

For Exercises $1-5,$ choose the correct letter.

What is the factored form of $2x^2+x-3$?

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

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

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

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

To determine

To factor the given equation.

Answer to Problem 2STP

  $2x^2+x-3=\left(x-1\right)\left(2x+3\right)$ & option F is correct.

Explanation of Solution

Given:

  $2x^2+x-3$

Calculation: The solution can be obtained as:

  $\begin{array}{l}2x^2+x-3=2x^2-2x+3x-3\\ =2x\left(x-1\right)+3\left(x-1\right)\\ =\left(x-1\right)\left(2x+3\right)\end{array}$

Hence option F is correct.