Solve 4v^3-5v^2-16v+20

$$4 v ^ { 3 } - 5 v ^ { 2 } - 16 v + 20$$

Factor

$$\left(v-2\right)\left(4v-5\right)\left(v+2\right)$$

Solution Steps

Do the grouping 4v^{3}-5v^{2}-16v+20=\left(4v^{3}-5v^{2}\right)+\left(-16v+20\right), and factor out v^{2} in the first and -4 in the second group.

$$v^{2}\left(4v-5\right)-4\left(4v-5\right)$$

Factor out common term 4v-5 by using distributive property.

$$\left(4v-5\right)\left(v^{2}-4\right)$$

Consider v^{2}-4. Rewrite v^{2}-4 as v^{2}-2^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(v-2\right)\left(v+2\right)$$

Rewrite the complete factored expression.

$$\left(4v-5\right)\left(v-2\right)\left(v+2\right)$$

Evaluate

$$\left(4v-5\right)\left(v^{2}-4\right)$$