Factor using the AC method..6x^3-4x^2-10x
first factor out an x.
2x(3x^2-2x-5)
Now you have a quadratic in the form of
(ax^2+bx+c)
2x(3x-5)(x+1)
To factor the expression 6x^3 - 4x^2 - 10x using the AC method, follow these steps:
Step 1: Look for the common factors.
In this case, the greatest common factor (GCF) is 2x, so we can factor out 2x from each term:
2x(3x^2 - 2x - 5)
Step 2: Find the product (AC) and the sum (B) of the coefficient of the quadratic term (x^2) and the constant term (the term without x).
AC = 3 * -5 = -15
B = -2
Step 3: Break down the product (AC) into two numbers whose sum is equal to B.
In this case, we need to find two numbers that multiply to -15 and add up to -2. The numbers that satisfy this condition are -5 and 3.
Step 4: Rewrite the quadratic term (-2x) using the two numbers found in Step 3.
Replace -2x with -5x + 3x:
2x(3x^2 - 5x + 3x - 5)
Step 5: Group the terms.
2x[(3x^2 - 5x) + (3x - 5)]
Step 6: Factor by grouping.
Take out the common factors from each group separately.
2x[x(3x - 5) + 1(3x - 5)]
Step 7: Identify the common binomial factor.
In this case, we have a common binomial factor of (3x - 5).
2x(3x - 5)(x + 1)
So, the factored form of the expression 6x^3 - 4x^2 - 10x using the AC method is 2x(3x - 5)(x + 1).