Question 4 (1 point) Which expression is equivalent to 2x^2+5x+4 a None of these b (2x+1)(x-4) C (2x+1)(x+4) d (2x-1)(x+4)

To determine which expression is equivalent to \(2x^2 + 5x + 4\), we need to expand each of the given options and see if any of them match the original expression.<br /><br />Let's start with option b: \((2x+1)(x-4)\).<br /><br />Expanding this expression:<br />\[<br />(2x+1)(x-4) = 2x \cdot x + 2x \cdot (-4) + 1 \cdot x + 1 \cdot (-4)<br />\]<br />\[<br />= 2x^2 - 8x + x - 4<br />\]<br />\[<br />= 2x^2 - 7x - 4<br />\]<br /><br />This does not match \(2x^2 + 5x + 4\).<br /><br />Next, let's try option c: \((2x+1)(x+4)\).<br /><br />Expanding this expression:<br />\[<br />(2x+1)(x+4) = 2x \cdot x + 2x \cdot 4 + 1 \cdot x + 1 \cdot 4<br />\]<br />\[<br />= 2x^2 + 8x + x + 4<br />\]<br />\[<br />= 2x^2 + 9x + 4<br />\]<br /><br />This does not match \(2x^2 + 5x + 4\).<br /><br />Finally, let's try option d: \((2x-1)(x+4)\).<br /><br />Expanding this expression:<br />\[<br />(2x-1)(x+4) = 2x \cdot x + 2x \cdot 4 - 1 \cdot x - 1 \cdot 4<br />\]<br />\[<br />= 2x^2 + 8x - x - 4<br />\]<br />\[<br />= 2x^2 + 7x - 4<br />\]<br /><br />This does not match \(2x^2 + 5x + 4\).<br /><br />Since none of the given options match the original expression \(2x^2 + 5x + 4\), the correct answer is:<br /><br />a) None of these