leonora is factoring a trinomial. the factors of the trinomial are shown on the model. which trinomial did…

leonora is factoring a trinomial. the factors of the trinomial are shown on the model. which trinomial did she factor? $x^{2}+4x - 12$ $x^{2}+2x - 6$ $x^{2}-8x - 6$ $x^{2}-4x - 12$

leonora is factoring a trinomial. the factors of the trinomial are shown on the model. which trinomial did she factor? $x^{2}+4x - 12$ $x^{2}+2x - 6$ $x^{2}-8x - 6$ $x^{2}-4x - 12$

Answer

Explanation:

Step1: Determine the factors

From the model, the factors are ((x + 2)) and ((x-6)) (since there is (+x) and (+x) which sum to (2x) in the expansion, and the constant terms: one positive unit is not there, but considering the standard factoring model interpretation where the length and width of the rectangle - like model for factoring gives the binomial factors. The general form of factoring a trinomial (ax^{2}+bx + c=(mx + p)(nx+q)), here (a = 1), and by visual inspection of the model (assuming standard area - model for factoring where the sides of the rectangle represent the binomial factors). The first binomial has (x) and a positive unit (count of (x) terms: one (x) from the top - left and one (x) from the left - hand side gives (x+2) when considering the sum of (x) terms in the expansion, and the constant terms: the negative units. The second binomial is (x-6)).

Step2: Expand the factors

Use the FOIL method ((a + b)(c + d)=ac+ad+bc+bd). For ((x + 2)(x - 6)), we have: [ \begin{align*} (x+2)(x - 6)&=x\times x+x\times(-6)+2\times x+2\times(-6)\ &=x^{2}-6x+2x-12\ &=x^{2}-4x - 12 \end{align*} ]

Answer:

(x^{2}-4x - 12) (the fourth option)