Solve v=(t-1)(t-3)(t-4)/(-1)(-2)(-4)

$$v = \frac { ( t - 1 ) ( t - 3 ) ( t - 4 ) } { ( - 1 ) ( - 2 ) ( - 4 ) }$$

Solve for v

$$v=-\frac{\left(t-4\right)\left(t-3\right)\left(t-1\right)}{8}$$

Solution Steps

Multiply -1 and -2 to get 2.

$$v=\frac{\left(t-1\right)\left(t-3\right)\left(t-4\right)}{2\left(-4\right)}$$

Multiply 2 and -4 to get -8.

$$v=\frac{\left(t-1\right)\left(t-3\right)\left(t-4\right)}{-8}$$

Use the distributive property to multiply t-1 by t-3 and combine like terms.

$$v=\frac{\left(t^{2}-4t+3\right)\left(t-4\right)}{-8}$$

Use the distributive property to multiply t^{2}-4t+3 by t-4 and combine like terms.

$$v=\frac{t^{3}-8t^{2}+19t-12}{-8}$$

Divide each term of t^{3}-8t^{2}+19t-12 by -8 to get -\frac{1}{8}t^{3}+t^{2}-\frac{19}{8}t+\frac{3}{2}.

$$v=-\frac{1}{8}t^{3}+t^{2}-\frac{19}{8}t+\frac{3}{2}$$