Question

If a(x) and b(x) are linear functions with one variable, which of the following expressions produces a quadratic function? (ab)(x) (a – b)(x) (a + b)(x)

Answer 1

For this case we have that by definition, a linear function is of the form $y = mx + b$

If we have that a and b are linear functions, then they are of the form:

$a (x) = mx + b\\b (x) = nx + c$

If we multiply them we have: (Applying distributive property)

$(mx + b) (nx + c) = (m * n) x ^ 2 + mcx + bnx + bc = (mn) x ^ 2 + (mc + bn) x + bc$

That is, we get a quadratic function.

Answer:

$(ab) (x)$