Original Expression: 6x² + 5x – 4 // Given trinomial

Step 1: Identify A, B, and C:

a. A = 6, B = 5, C = -4 // Coefficients of the trinomial

Step 2: Multiply A and C:

b. AC = 6 * (-4) = -24 // Product of A and C

Step 3: Find two numbers whose product is AC and sum is B:

c. 8 and -3 // Numbers that multiply to -24 and add to 5

Step 4: Split the middle term using the numbers found:

d. 6x² + 8x – 3x – 4 // Splitting the middle term

Step 5: Group the terms:

e. (6x² + 8x) + (-3x – 4) // Grouping in pairs

Step 6: Factor out the GCF from each group:

f. 2x(3x + 4) – 1(3x + 4) // Factoring out the GCF

Step 7: Factor by grouping:

g. (2x – 1)(3x + 4) // Final factored form

Final Expression: (2x – 1)(3x + 4) // Final result

Original Expression: 3x² – 7x – 6 // Given trinomial

Step 1: Identify A, B, and C:

a. A = 3, B = -7, C = -6 // Coefficients of the trinomial

Step 2: Multiply A and C:

b. AC = 3 * (-6) = -18 // Product of A and C

Step 3: Find two numbers whose product is AC and sum is B:

c. 9 and -2 // Numbers that multiply to -18 and add to -7

Step 4: Split the middle term using the numbers found:

d. 3x² + 9x – 2x – 6 // Splitting the middle term

Step 5: Group the terms:

e. (3x² + 9x) + (-2x – 6) // Grouping in pairs

Step 6: Factor out the GCF from each group:

f. 3x(x + 3) – 2(x + 3) // Factoring out the GCF

Step 7: Factor by grouping:

g. (3x – 2)(x + 3) // Final factored form

Final Expression: (3x – 2)(x + 3) // Final result