Question

Factor this polynomial. 6a^2 -13ab-5b^2. Where do I even begin!?

Answer 1

Factor this polynomial.

`6a^2-13ab-5b^(2.)`

Notice that:

`-13ab=2ab-15ab\text{.}`

Then:

`6a^2-13ab-5b^(2.)=6a^2+2ab-15ab-5b^2\text{.}`

Now, notice that:

`\begin{gathered} 6a^2+2ab=2a(3a+b), \\ -15ab-5b^2=-5b(3a+b)\text{.} \end{gathered}`

Therefore:

`6a^2-13ab-5b^2=2a(3a+b)-5b(3a+b)\text{.}`

Grouping the above result we get that:

`6a^2-13ab-5b^(2.)=(2a-5b)(3a+b)\text{.}`

Answer:

`6a^2-13ab-5b^(2.)=(2a-5b)(3a+b)\text{.}`