Final answer:
The expression 2x^4 + 22x^2 + 56x is factored by finding the GCF, which is 2x, resulting in 2x(x^3 + 11x + 28), which is then further factored down to 2x(x + 4)(x + 7).
Step-by-step explanation:
The student is asking about factoring a polynomial expression. To factor the expression 2x^4 + 22x^2 + 56x, we must first find the greatest common factor (GCF) that each term shares. In this case, each term has at least one factor of 2x, so we factor 2x out of each term.
After factoring out 2x, we have:
2x(x^3 + 11x + 28)
This can be further factored since the quadratic expression inside the parentheses is factorable:
2x(x + 4)(x + 7)
Thus, the expression is completely factored and the correct answer is:
c) 2x(x^2 + 11x + 28)