the diagram represents the factorization of a²+8a+12. what is the missing number that will complete the…
the diagram represents the factorization of a²+8a+12. what is the missing number that will complete the factorization? o 6 o 8 o 12 o 24
Answer
Explanation:
Step1: Recall factoring quadratic form
We know that (a^{2}+8a + 12=(a + m)(a + n)=a^{2}+(m + n)a+mn).
Step2: Analyze the given diagram
From the diagram, we have one factor as ((a + 2)). Let the other factor be ((a + x)). Then ((a + 2)(a + x)=a^{2}+(2 + x)a+2x).
Step3: Compare coefficients
We know that (2x = 12), so (x=\frac{12}{2}=6). Also, (2 + x=8) when (x = 6). And (6a) in the diagram is the product of (a) and (6).
Answer:
A. 6