mia is factoring the polynomial $x^{2}+4x - 12$. she uses the steps shown. in which step did mia make an…

mia is factoring the polynomial $x^{2}+4x - 12$. she uses the steps shown. in which step did mia make an error? step 1: $x^{2}+6x - 2x - 12$; step 2: $(x^{2}+6x)-(2x + 12)$; step 3: $x(x + 6)-2(x + 6)$; step 4: $(x + 6)(x + 2)$

mia is factoring the polynomial $x^{2}+4x - 12$. she uses the steps shown. in which step did mia make an error? step 1: $x^{2}+6x - 2x - 12$; step 2: $(x^{2}+6x)-(2x + 12)$; step 3: $x(x + 6)-2(x + 6)$; step 4: $(x + 6)(x + 2)$

Answer

Explanation:

Step 1: Check polynomial factorization steps

Original polynomial: (x^2 + 4x - 12).
Step 1 splits (4x) into (6x - 2x), which is correct since (6 \times (-2) = -12) and (6 + (-2) = 4).

Step 2: Verify grouping

Step 2 groups as ((x^2 + 6x) - (2x + 12)). Correctly applies parentheses with a negative sign to maintain (-2x - 12).

Step 3: Check factoring out common terms

Step 3 factors as (x(x + 6) - 2(x + 6)). Correctly extracts (x) from the first group and (-2) from the second group.

Step 4: Identify final factoring error

Step 4 writes ((x + 6)(x + 2)). The correct factorization should be ((x + 6)(x - 2)) because (-2(x + 6)) leaves a (-2), not (+2).

Answer:

Step 4