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{`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)}}`

________

#LetsStudy

Answer 2

(x-6) (x-4)

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)