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Question

What is the expression in factored form?

2x2+x−3

Answer 1

To factor the expression 2x^2 + x - 3, we need to find two binomials whose product is equal to the expression.

First, we look for two numbers whose product is 2 * -3 = -6 and whose sum is 1 (the coefficient of x). The numbers that satisfy these conditions are 3 and -2.

We can rewrite the expression as:

2x^2 + 3x - 2x - 3

Now, we group the terms and factor out the greatest common factor from each group:

x(2x + 3) - 1(2x + 3)

Notice that we have a common binomial (2x + 3) in both terms. We can factor it out:

(2x + 3)(x - 1)

Thus, the expression 2x^2 + x - 3 is factored as (2x + 3)(x - 1).