Question

Write a linear factorization of the function. f(x) = 49x4 + x2.

Answer 1

The linear factorization of the function f(x) = 49x^4 + x^2 is f(x) = x^2(49x^2 + 1).

Step-by-step explanation:

The function f(x) = 49x4 + x2 can be factorized by recognizing that it is a quadratic expression. We can factor out a common factor of x2 to get:

f(x) = x2(49x2 + 1)

Now, the expression 49x2 + 1 cannot be further factored as it is a sum of squares. Therefore, the linear factorization of the function f(x) = 49x4 + x2 is f(x) = x2(49x2 + 1).