# How do you factor 28x^3 +17x^2 -30x + 6?

Refer to explanation

#### Explanation:

Using the following "clever" method

We try to factor it as a product of a polynomial of first degree and one of second degree as follows

$28 {x}^{3} + 17 {x}^{2} - 30 x + 6 = \left(4 x + a\right) \cdot \left(7 {x}^{2} + b x + c\right)$

Now doing the calculation in the RHS of the equation and equating the correspoding parts we get

$a = - 1 , b = 6 , c = - 6$ hence

$28 {x}^{3} + 17 {x}^{2} - 30 x + 6 = \left(4 x - 1\right) \cdot \left(7 {x}^{2} + 6 x - 6\right)$

It is easy to factor $7 {x}^{2} + 6 x - 6$ as well hence we have that

$28 {x}^{3} + 17 {x}^{2} - 30 x + 6 = \left(4 x - 1\right) \cdot \left[- \frac{1}{7} \cdot \left(- 7 x + \sqrt{51} - 3\right) \cdot \left(7 x + \sqrt{51} + 3\right)\right]$