Type your answers to each problem in the table below. The order of the factors doesn't matter, but use parentheses around each one!

Question

2x^2 + 5x - 3

Answer 1

To factor the quadratic expression \( 2x^2 + 5x - 3 \), we will use the method of factoring by grouping.

1. Multiply the coefficient of \( x^2 \) (which is 2) by the constant term (which is -3). This gives us: \( 2 \times -3 = -6 \).

2. We need to find two numbers that multiply to -6 and add to the coefficient of \( x \) (which is 5). The numbers that satisfy this condition are 6 and -1.

3. Rewrite the expression using these two numbers to split the middle term: \[ 2x^2 + 6x - 1x - 3 \]

4. Now group the terms: \[ (2x^2 + 6x) + (-1x - 3) \]

5. Factor out common factors from each group: \[ 2x(x + 3) - 1(x + 3) \]

6. Now we can factor out the common binomial factor \( (x + 3) \): \[ (2x - 1)(x + 3) \]

Thus, the factored form of the expression \( 2x^2 + 5x - 3 \) is:

\[ (2x - 1)(x + 3) \]