Problem:
Describe how you would factor.
[tex]\tt{ {x}^{2} - 10x + 24}[/tex]
Let's Solve it!
To factorize [tex]\tt{ {a}^{2} + bx + c = 0 }[/tex]we split [tex]\tt{"ac"}[/tex]into two factors, whose sum is b. In polynomial [tex]\tt{ {x}^{2} - 10x + 24}[/tex], the product is 24 and hence such factors would be -6 and -4. Hence splitting middle term this way.
We get this:
[tex]\quad\tt{ {x}^{2} - 10x + 24 = {x}^{2} - 6x - 4x + 24.i.e}[/tex]
[tex]\quad\tt{ x(x - 6) - 4(x - 6)} \: \: or[/tex]
[tex]\quad\quad\quad\quad\tt{ (x - 6)(x - 4)}[/tex]
Hence, The answer is,
[tex]\quad\quad\quad\quad \boxed{\tt{ \color{green}(x - 6)(x - 4)}}[/tex]
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