Answer: \((5x+1)(2x-1)\)
Solution: Need factors of \(10\cdot(-1)\) that add up to \(-3\).
Those factors are \(-5\) and \(2\), so we need to place them in parentheses in such a way that the inner terms multiply to \(2x\) and the outer terms multiply to \(-5x\):
\[ ( \quad \quad \qquad )( \quad \quad \quad )\]
\(10x^2\) has factors of \(5x\) and \(2x\), which we can place in our parentheses like below.
\[ (5x\quad \quad )(2x\quad \quad )\]
The outer terms should still multiply to \(-5x\) and the inner terms to \(2x\). \(1\) obviously has factors of \(1\) and \(1\), so...
\[ (5x \quad 1)(2x \quad 1)\]
Since the product of the outside two numbers needs to be \(-5x\) and the inner two numbers need to have a product of \(2x\), we get
\[ (5x + 1)(2x - 1)\]