factor using Ac Method 9x^2-6x-8
Don't know what you call the Ac method, but on the third trial-and-error I got
(3x+2)(3x-4)
To factor the quadratic expression 9x^2 - 6x - 8 using the AC method, follow these steps:
Step 1: Check the coefficients.
First, identify the values of a, b, and c in the quadratic expression: ax^2 + bx + c.
In this case, a = 9, b = -6, and c = -8.
Step 2: Multiply the coefficients a and c.
Multiply the values of a and c: 9 * -8 = -72.
This product will be needed in the next steps.
Step 3: Find two numbers.
Find two numbers that multiply to give the product -72 and add up to the coefficient of b, which is -6.
In this case, the two numbers are -12 and +6 because:
-12 * 6 = -72 (product) and -12 + 6 = -6 (sum of coefficients).
Step 4: Rewrite the quadratic expression.
Split the middle term (-6x) using the two numbers found in step 3. Replace -6x with -12x + 6x. This rewriting helps in factoring by grouping.
Now, the quadratic expression becomes:
9x^2 - 12x + 6x - 8
Step 5: Group and factor by common terms.
Group the terms in pairs and factor out the common terms from each pair.
(9x^2 - 12x) + (6x - 8)
Taking out the greatest common factor (GCF) from each pair:
3x(3x - 4) + 2(3x - 4)
Step 6: Factor out the common binomial.
Notice that (3x - 4) is common in both grouped terms.
Factor out the common binomial (3x - 4):
(3x - 4)(3x + 2)
Therefore, the factored form of the quadratic expression 9x^2 - 6x - 8 using the AC method is (3x - 4)(3x + 2).