Question

#6. Factor completely.
Type your answers to each problem in the table below. The order of the factors doesn't matter, but use parentheses around each one! 2x^2 + x - 10

Answer 1

To factor the quadratic expression \(2x^2 + x - 10\), we can follow these steps:

1. Multiply the leading coefficient (2) by the constant term (-10):
\[
2 \times -10 = -20.
\]

2. We need to find two numbers that multiply to -20 and add up to the middle coefficient (1). The numbers that satisfy this are:
\[
5 \text{ and } -4.
\]

3. Rewrite the middle term (x) using these two numbers:
\[
2x^2 + 5x - 4x - 10.
\]

4. Now, group the terms:
\[
(2x^2 + 5x) + (-4x - 10).
\]

5. Factor out the common factors in each group:
\[
x(2x + 5) - 2(2x + 5).
\]

6. Now, factor out the common binomial factor \((2x + 5)\):
\[
(2x + 5)(x - 2).
\]

So, the completely factored form of the expression \(2x^2 + x - 10\) is:
\[
(2x + 5)(x - 2).
\]

### Final Answer
\[
(2x + 5)(x - 2)
\]