Determine the resulting polynomial: f(x)=7x+9 g(x)=5x^2+7x-9 Find: f(x)cdot g(x) Answer Attemptiout of 2 square

To find the resulting polynomial \( f(x) \cdot g(x) \), we need to multiply the two given polynomials \( f(x) \) and \( g(x) \).<br /><br />Given:<br />\[ f(x) = 7x + 9 \]<br />\[ g(x) = 5x^2 + 7x - 9 \]<br /><br />We will use the distributive property to multiply each term in \( f(x) \) by each term in \( g(x) \):<br /><br />\[<br />f(x) \cdot g(x) = (7x + 9) \cdot (5x^2 + 7x - 9)<br />\]<br /><br />First, distribute \( 7x \):<br /><br />\[<br />7x \cdot 5x^2 = 35x^3<br />\]<br />\[<br />7x \cdot 7x = 49x^2<br />\]<br />\[<br />7x \cdot (-9) = -63x<br />\]<br /><br />Next, distribute \( 9 \):<br /><br />\[<br />9 \cdot 5x^2 = 45x^2<br />\]<br />\[<br />9 \cdot 7x = 63x<br />\]<br />\[<br />9 \cdot (-9) = -81<br />\]<br /><br />Now, combine all these terms:<br /><br />\[<br />f(x) \cdot g(x) = 35x^3 + 49x^2 - 63x + 45x^2 + 63x - 81<br />\]<br /><br />Combine like terms:<br /><br />\[<br />f(x) \cdot g(x) = 35x^3 + (49x^2 + 45x^2) + (-63x + 63x) - 81<br />\]<br /><br />Simplify:<br /><br />\[<br />f(x) \cdot g(x) = 35x^3 + 94x^2 + 0x - 81<br />\]<br /><br />So, the resulting polynomial is:<br /><br />\[<br />\boxed{35x^3 + 94x^2 - 81}<br />\]