Question

Factor completely
Ex) 2x^2 + 5x -3: (2x -1) (x+3)
6) 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. **Find two numbers that multiply to -20 and add up to the middle coefficient (1)**:
The numbers that satisfy this are 5 and -4 because:
\[
5 \times -4 = -20 \quad \text{and} \quad 5 + (-4) = 1
\]

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

4. **Group the terms**:
\[
(2x^2 + 5x) + (-4x - 10)
\]

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

6. **Notice that \(2x + 5\) is a common factor**:
\[
(2x + 5)(x - 2)
\]

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