Question

factor the polynomial, if possible. drag the expressions into the box if they are part of the factored form of the polynomial. if the polynomial cannot be factored, drag prime. 6x² + 4x - 16

Explanation:

Step1: Factor out the GCF

First, find the greatest common factor (GCF) of the terms \(6x^2\), \(4x\), and \(-16\). The GCF of 6, 4, and 16 is 2. So we factor out 2:
\(6x^2 + 4x - 16 = 2(3x^2 + 2x - 8)\)

Step2: Factor the quadratic

Now, factor the quadratic \(3x^2 + 2x - 8\). We need two numbers that multiply to \(3\times(-8)= -24\) and add up to 2. The numbers are 6 and -4.
Rewrite the middle term using these numbers:
\(3x^2 + 6x - 4x - 8\)

Step3: Group and factor

Group the first two terms and the last two terms:
\((3x^2 + 6x) + (-4x - 8)\)
Factor out the GCF from each group:
\(3x(x + 2) - 4(x + 2)\)

Step4: Factor out the common binomial

Now, factor out the common binomial \((x + 2)\):
\((3x - 4)(x + 2)\)

Step5: Combine with the GCF

Putting it all together with the GCF we factored out earlier:
\(2(3x - 4)(x + 2)\)

Answer:

\(2(3x - 4)(x + 2)\)