Question

Which polynomial function has a leading coefficient of 3 and roots 4, I, and 2, all with multiplicity 1? Of(x) = 3(x + 4)(x - 1)(x - 2) O f(x) = (x - 3)(x + 4)(x - 1)(x - 2) f(x) = (x - 3)(x + 4)(x - 1)(x + 1)(x - 2) O f(x) = 3(x + 4)(x - 1)(x + 1)(x - 2) N​

Answer 1

A

Explanation:

Just did it

Answer 2

Note: There must be -4 instead of 4 otherwise all options are incorrect.

Given:

A polynomial function has a leading coefficient of 3 and roots -4, 1, and 2, all with multiplicity 1.

To find:

The polynomial function.

Solution:

The general polynomial function is defined as:

`P(x)=a(x-c_1)^(m_1)(x-c_2)^(m_2)...(x-c_n)^(m_n)`

Where, a is the leading coefficient,
`c_1,c_2,...,c_n` are the zeros with multiplicity
`m_1,m_2,...,m_n` respectively.

It is given that a polynomial function has a leading coefficient of 3 and roots 4, 1, and 2, all with multiplicity 1. So, the polynomial function is defined as:

`P(x)=3(x-(-4))^1(x-1)^1(x-2)^1`

`P(x)=3(x+4)(x-1)(x-2)`

Therefore, the correct option is A.