To factor the trinomial \(2x^2 + x - 10\), we need to find two numbers that multiply to \(2 \times (-10) = -20\) and add up to \(1\) (the coefficient of \(x\)).
The two numbers that satisfy these conditions are \(5\) and \(-4\) because:
- \(5 + (-4) = 1\)
- \(5 \times (-4) = -20\)
Now we can rewrite the middle term \(x\) using these two numbers:
\[ 2x^2 + 5x - 4x - 10 \]
Next, we group the terms:
\[ (2x^2 + 5x) + (-4x - 10) \]
Now, factor out the common factors from each group:
\[ x(2x + 5) - 2(2x + 5) \]
Now, factor out the common binomial factor \((2x + 5)\):
\[ (2x + 5)(x - 2) \]
Thus, the factored form of the trinomial \(2x^2 + x - 10\) is:
\[ (2x + 5)(x - 2) \]
So the answers are:
- \(2x + 5\)
- \(x - 2\)
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