Q. 375 - Intermediate Algebra

Question

In the following exercise, factor.

$15x^2 + 6x - 2$

Step-by-Step Solution

Answer

The given polynomial is prime and cannot be factorised.

Step 1. Given information

The given expression is :

$15x^2 + 6x - 2$

Step 2. Use ac method for factorisation

To factorise the polynomial $a{x}^2+bx+c$ by $ac$ method, we need to think of two numbers whose product is equal to $ac$ and the sum is equal to  $b$.

For polynomial $15x^2+ 6x-2$ we have:

$$\begin{gathered} ac=15\times (-2) \\ =-30 \end{gathered}$$

And we have to think of two numbers whose sum is equal to $6$ and product is equal to $-30$.

Then there are no two numbers whose sum is $6$ and the product is $-30$.

Thus, this trinomial is prime.