Question

Describe how you would factor x^2 - 10x + 24. Be specific.

Answer 1

Problem:

Describe how you would factor.

$\tt{ {x}^{2} - 10x + 24}$

Let's Solve it!

To factorize $\tt{ {a}^{2} + bx + c = 0 }$we split $\tt{"ac"}$into two factors, whose sum is b. In polynomial $\tt{ {x}^{2} - 10x + 24}$, the product is 24 and hence such factors would be -6 and -4. Hence splitting middle term this way.

We get this:

$\quad\tt{ {x}^{2} - 10x + 24 = {x}^{2} - 6x - 4x + 24.i.e}$

$\quad\tt{ x(x - 6) - 4(x - 6)} \: \: or$

$\quad\quad\quad\quad\tt{ (x - 6)(x - 4)}$

Hence, The answer is,

$\quad\quad\quad\quad \boxed{\tt{ \color{green}(x - 6)(x - 4)}}$

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Answer 2

Answer:

(x-6) (x-4)

Step-by-step explanation:

x^2 - 10x + 24

What two number multiply to 24 and add to -10

-6*-4 = 24

-6+-4 = -10

(x-6) (x-4)