Question

How to factor 3x^2-9x-84

Answer 1

To solve a question like this, you will need to factorise the first term of the expression out.

So, our expression becomes

`3(x^2\text{ }-3x-28)\text{ }`

Now, you will need to find the factors of 28 whose sum will give you -3

Always remember to express it in terms of x.

The answer to that is -7x and +4x. Thus we can rewrite the expression as;

`\begin{gathered} 3(x^2-7x+4x-28) \\ 3\left\lbrace x(x-7)+4(x-7)\right\rbrace \text{ }\Longrightarrow\text{ By factorizing the terms of the expression } \\ 3\left\lbrace x(x-7)+4(x-7)\right\rbrace \text{ }\Longrightarrow\text{which can further be factorized as} \\ 3(x-4)(x-7) \end{gathered}`

In summary 3x^2-9x-84​ can be factorized as

`3(x-4)(x-7)`