Solve 4q^3-20q^2-200q

$$4 q ^ { 3 } - 20 q ^ { 2 } - 200 q$$

Factor

$$4q\left(q-10\right)\left(q+5\right)$$

Solution Steps

Factor out 4.

$$4\left(q^{3}-5q^{2}-50q\right)$$

Consider q^{3}-5q^{2}-50q. Factor out q.

$$q\left(q^{2}-5q-50\right)$$

Consider q^{2}-5q-50. Factor the expression by grouping. First, the expression needs to be rewritten as q^{2}+aq+bq-50. To find a and b, set up a system to be solved.

$$a+b=-5 ab=1\left(-50\right)=-50$$

Since ab is negative, a and b have the opposite signs. Since a+b is negative, the negative number has greater absolute value than the positive. List all such integer pairs that give product -50.

$$1,-50 2,-25 5,-10$$

Calculate the sum for each pair.

$$1-50=-49 2-25=-23 5-10=-5$$

The solution is the pair that gives sum -5.

$$a=-10 b=5$$

Rewrite q^{2}-5q-50 as \left(q^{2}-10q\right)+\left(5q-50\right).

$$\left(q^{2}-10q\right)+\left(5q-50\right)$$

Factor out q in the first and 5 in the second group.

$$q\left(q-10\right)+5\left(q-10\right)$$

Factor out common term q-10 by using distributive property.

$$\left(q-10\right)\left(q+5\right)$$

Rewrite the complete factored expression.

$$4q\left(q-10\right)\left(q+5\right)$$

Evaluate

$$4q\left(q-10\right)\left(q+5\right)$$