Answer:
The ecuation factored is (x-3)(x-8)
Step-by-step explanation:
- First, consider that you can express any type of 2 grade polynomial in terms of (x-x₁)(x-x₂) where x₁ and x₂ are numbers or constants
- In this example the polynomial [tex]x^{2}-11 x+24[/tex] is a 2 grade polynomial, you can notice that by the mayor exponent in x is 2 ([tex]x^2[/tex]), so one technique to factor a 2 grade polynomial is using the cuadratic formula [tex]x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}[/tex] where a,b are the coefficients and c is the independent term of [tex]a x^2 + b x + c = 0[/tex]
- Having all the formulas and replacing a=1, b=11 and c=24:
[tex]x = \frac {- (11) \pm \sqrt {(- 11)^2 - 4 1 24}}{2 1}[/tex]
This results in two values X₁=8 and X₂=3 ⇒ Replacing in (x-x₁)(x-x₂)
⇒ Gives: (x-8)(x-3)
