Solve 10x^3+95x^2+175x

$$10 x ^ { 3 } + 95 x ^ { 2 } + 175 x$$

Factor

$$5x\left(x+7\right)\left(2x+5\right)$$

Solution Steps

Factor out 5.

$$5\left(2x^{3}+19x^{2}+35x\right)$$

Consider 2x^{3}+19x^{2}+35x. Factor out x.

$$x\left(2x^{2}+19x+35\right)$$

Consider 2x^{2}+19x+35. Factor the expression by grouping. First, the expression needs to be rewritten as 2x^{2}+ax+bx+35. To find a and b, set up a system to be solved.

$$a+b=19 ab=2\times 35=70$$

Since ab is positive, a and b have the same sign. Since a+b is positive, a and b are both positive. List all such integer pairs that give product 70.

$$1,70 2,35 5,14 7,10$$

Calculate the sum for each pair.

$$1+70=71 2+35=37 5+14=19 7+10=17$$

The solution is the pair that gives sum 19.

$$a=5 b=14$$

Rewrite 2x^{2}+19x+35 as \left(2x^{2}+5x\right)+\left(14x+35\right).

$$\left(2x^{2}+5x\right)+\left(14x+35\right)$$

Factor out x in the first and 7 in the second group.

$$x\left(2x+5\right)+7\left(2x+5\right)$$

Factor out common term 2x+5 by using distributive property.

$$\left(2x+5\right)\left(x+7\right)$$

Rewrite the complete factored expression.

$$5x\left(2x+5\right)\left(x+7\right)$$

Evaluate

$$5x\left(x+7\right)\left(2x+5\right)$$