Completely factor the following expression.
1.4x^2-8x-12+6x
First combine like terms.
4x^2-8x-12+6x = 4x^2 -2x -12 = (4x+6)(x-2)
To completely factor the expression 1.4x^2 - 8x - 12 + 6x, we start by combining like terms:
1.4x^2 - 8x - 12 + 6x
Simplifying further:
= 1.4x^2 - 2x - 12
Next, we need to find two numbers that multiply to give -16.8 (which is the product of 1.4 and -12) and add up to -2 (which is the coefficient of x).
Let's use a factorization method called "splitting the middle term." We can rewrite -2x as the sum of two terms:
-2x = (-4x) + (2x)
Now, the expression becomes:
= 1.4x^2 - 4x + 2x - 12
We can group the terms:
= (1.4x^2 - 4x) + (2x - 12)
Now, we can factor common terms from each group:
= x(1.4x - 4) + 2(1.4x - 4)
Notice that we have a common factor of (1.4x - 4) in both terms. We can factor it out:
= (x + 2)(1.4x - 4)
Therefore, the completely factored expression is (x + 2)(1.4x - 4).