tô Multiple Choice 5 points f(t)=t^2+2t g(t)=4t-1 Find (fcdot g)(t) 4t^3+7t^2-2t 6t^3-t^2-15t -8t^2-6t+5 -3t^4+3t^3-15t^2+15t 1 Multiple Choice 5 points g(a)=3a+1 h(a)=a^2-a Find g(a)cdot h(a) -6a^4-9a^3-10a^2-15a -3a^3-2a^2+a 3a^3-2a^2-a 4a^3+6a^2-4a

### Question 1: Find \((f \cdot g)(t)\)<br /><br />We are given:<br />\[<br />f(t) = t^2 + 2t, \quad g(t) = 4t - 1<br />\]<br />To find \((f \cdot g)(t)\), we multiply \(f(t)\) and \(g(t)\):<br />\[<br />(f \cdot g)(t) = f(t) \cdot g(t) = (t^2 + 2t)(4t - 1)<br />\]<br /><br />Using the distributive property:<br />\[<br />(t^2 + 2t)(4t - 1) = t^2(4t - 1) + 2t(4t - 1)<br />\]<br />\[<br />= (4t^3 - t^2) + (8t^2 - 2t)<br />\]<br />\[<br />= 4t^3 + 7t^2 - 2t<br />\]<br /><br />Thus, the correct answer is:<br />\[<br />\boxed{4t^3 + 7t^2 - 2t}<br />\]<br /><br />---<br /><br />### Question 2: Find \(g(a) \cdot h(a)\)<br /><br />We are given:<br />\[<br />g(a) = 3a + 1, \quad h(a) = a^2 - a<br />\]<br />To find \(g(a) \cdot h(a)\), we multiply \(g(a)\) and \(h(a)\):<br />\[<br />g(a) \cdot h(a) = (3a + 1)(a^2 - a)<br />\]<br /><br />Using the distributive property:<br />\[<br />(3a + 1)(a^2 - a) = 3a(a^2 - a) + 1(a^2 - a)<br />\]<br />\[<br />= 3a^3 - 3a^2 + a^2 - a<br />\]<br />\[<br />= 3a^3 - 2a^2 - a<br />\]<br /><br />Thus, the correct answer is:<br />\[<br />\boxed{3a^3 - 2a^2 - a}<br />\]