Question

Can a trinomial with a leading coefficient not equal to 1 have two identical factors? If so, give an example.​

Answer 1

Using the Factor Theorem, it is found that it is possible for a trinomial with a leading coefficient not equal to 1 have two identical factors, and an example is:

$f(x) = 2(x - 1)^2(x - 2)$

The Factor Theorem states that a polynomial function with roots $x_1, x_2, \codts, x_n$ is given by:

$f(x) = a(x - x_1)(x - x_2) \cdots (x - x_n)$

• In which a is the leading coefficient.

In this problem:

• Leading coefficient of $a = 2$.

• Identical factors at x = 1, hence $x_1 = x_2 = 1$.

• A trinomial has three factors, hence for example another one at x = 3, hence $x_3 = 3$

Then, the example of the trinomial is:

$f(x) = 2(x - 1)^2(x - 2)$

You can learn more about the Factor Theorem at https://brainly.com/question/24380382