Question

Factor completely. x^2−11x+24 Enter your answer in the box.

Answer 1

The problem factored is (x-8)(x-3)

Answer 2

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 $x^{2}-11 x+24$  is a 2 grade polynomial, you can notice that by the mayor exponent in x is 2 ($x^2$), so one technique to factor a 2 grade polynomial is using the cuadratic formula $x = \frac {-b \pm \sqrt {b^2 - 4ac}}{2a}$ where a,b are the coefficients and c is the independent term of $a x^2 + b x + c = 0$

• Having all the formulas and replacing a=1, b=11 and c=24:

$x = \frac {- (11) \pm \sqrt {(- 11)^2 - 4 1 24}}{2 1}$

This results in two values X₁=8 and X₂=3 ⇒ Replacing in (x-x₁)(x-x₂)

⇒  Gives:  (x-8)(x-3)