Solve 5x^3-15x^2-1700x

$$5 x ^ { 3 } - 15 x ^ { 2 } - 1700 x$$

Factor

$$5x\left(x-20\right)\left(x+17\right)$$

Solution Steps

Factor out 5.

$$5\left(x^{3}-3x^{2}-340x\right)$$

Consider x^{3}-3x^{2}-340x. Factor out x.

$$x\left(x^{2}-3x-340\right)$$

Consider x^{2}-3x-340. Factor the expression by grouping. First, the expression needs to be rewritten as x^{2}+ax+bx-340. To find a and b, set up a system to be solved.

$$a+b=-3 ab=1\left(-340\right)=-340$$

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 -340.

$$1,-340 2,-170 4,-85 5,-68 10,-34 17,-20$$

Calculate the sum for each pair.

$$1-340=-339 2-170=-168 4-85=-81 5-68=-63 10-34=-24 17-20=-3$$

The solution is the pair that gives sum -3.

$$a=-20 b=17$$

Rewrite x^{2}-3x-340 as \left(x^{2}-20x\right)+\left(17x-340\right).

$$\left(x^{2}-20x\right)+\left(17x-340\right)$$

Factor out x in the first and 17 in the second group.

$$x\left(x-20\right)+17\left(x-20\right)$$

Factor out common term x-20 by using distributive property.

$$\left(x-20\right)\left(x+17\right)$$

Rewrite the complete factored expression.

$$5x\left(x-20\right)\left(x+17\right)$$

Evaluate

$$5x\left(x-20\right)\left(x+17\right)$$