Respuesta :
The factored form of the considered polynomial is [tex](x+3)(x+8)[/tex]
How to find the factors of a quadratic expression?
If the given quadratic expression is of the form
[tex]ax^2 + bx + c[/tex]
then its factored form is obtained by two numbers alpha( α ) and beta( β) such that:
[tex]b = \alpha + \beta \\ ac =\alpha \times \beta[/tex]
Then writing b in terms of alpha and beta would help us getting common factors out.
For the considered polynomial, we've got the quadratic expression as:
[tex]x^2 + 11x + 24[/tex]
Comparing this with [tex]ax^2 + bx + c[/tex], we get:
- a = 1 (since [tex]x^2 = 1\times x^2[/tex] )
- b = 11
- c= 24
Therefore, we have : ac = c = 24
Two numbers whose multiplication gives 24 and and whose addition gives 11.
24 = [tex]2 \times 2 \times 2 \times 3[/tex]
If we take first three 2s, and 3, then:
[tex]24 = 8 \times 3 = (2 \times 2 \times 2) \times 3\\11 = 8 + 3 = (2 \times 2 \times 2) + 3[/tex]
Thus, we need to write 11 in the middle in terms of 8 and 3:
[tex]x^2 + 11x + 24 = x^2 + 8x + 3x + 24 = x(x+8) + 3(x+8) = (x+3)(x+8)[/tex]
Thus, the factored form of the considered polynomial is [tex](x+3)(x+8)[/tex]
Learn more about factors of a quadratic equations here:
https://brainly.com/question/26675692
