# How do you factor 3x^2–11x–4?

Mar 4, 2018

$\left(x - 4\right) \left(3 x + 1\right)$

#### Explanation:

To factor this quadratic, you need a generic rectangle and a diamond problem

First, we need to find the sum and product of the diamond problem. To find the product, multiply $3 {x}^{2}$ by $- 4$. The product of the diamond problem is $- 12 {x}^{2}$. The sum of the diamond problem is $- 11 x$. Now that we know what the sum and product of the diamond problem is, we need to find two terms that multiply to get $- 12 {x}^{2}$ and adds to $- 11 x$. The two numbers are $- 12 x$ and $x$.

We can now insert our terms into the generic rectangle. The first term of the quadratic goes on the bottom left square and the last term goes to the top right square. The two terms from the diamond problem will go in the other two squares. The numbers on the bottom side of the generic rectangle will multiply by the numbers on the left side. Therefore, the factored form of this quadratic is $\left(x - 4\right) \left(3 x + 1\right)$

Now that we know what the factored form of this quadratic is, we can check our answer
$\left(x - 4\right) \left(3 x + 1\right)$
$3 {x}^{2} + x - 12 x - 4$
$3 {x}^{2} - 11 x - 4$ (correct)