Question

#6. Factor completely.
X
Type your answers to each problem in the table below. The order of the factors doesn't matter, but use parentheses around each one!
Ex) 2x ^ 2 + 5x - 3
6) 2x ^ 2 + x - 10
Example
(2x-1)
Correct?
(x + 3)

Answer 1

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

1. Look for two numbers that multiply to \(a \cdot c\) (where \(a\) is the coefficient of \(x^2\) and \(c\) is the constant term) and add to \(b\) (the coefficient of \(x\)). Here, \(a = 2\), \(b = 1\), and \(c = -10\). So, we need two numbers that multiply to \(2 \cdot (-10) = -20\) and add up to \(1\).

2. The two numbers that meet these criteria are 5 and -4 since \(5 \times (-4) = -20\) and \(5 + (-4) = 1\).

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

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

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

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

So, the complete factorization of \(2x^2 + x - 10\) is:
\[
(2x + 5)(x - 2)
\]

You can enter the answer as:
(2x + 5)(x - 2)