Question

G(x)=2x^3 5x^2-28x-15

Answer 1

Certainly! If \((x-3)\) is a factor of the polynomial function
`\(g(x) = 2x^3 + 5x^2 - 28x - 15\)`, it means that
`\(g(3) = 0\)`. We can use synthetic division to verify this.

Starting with the coefficients of
`\(g(x)\)`, which are 2, 5, -28, and -15, we perform synthetic division:

```

3 | 2 5 -28 -15

| 0 6 33 15

---------------------

2 11 5

```

The remainder is 5, which means
`\(g(3) = 5\)`, and since it's not equal to zero, there was an error. Apologies for any confusion.

Let's correct it:

We want
`\((x - 3)\)` to be a factor, so we need to find the correct factorization:

`\((x - 3)(2x^2 + 11x + 5)\)`

So, the corrected equation for
`\(g\)` as the product of linear factors is:

`\[g(x) = (x - 3)(2x^2 + 11x + 5)\]`

The probable question may be:

Find the roots of the polynomial function 2x^3 + 5x^2 - 28x - 15.