Question

Help please I don't know

Answer 1

The first row multiplication of
`(4x^3 + 0x^2 - 3x + 4)` and
`(2x - 5)` results in
`-20x^3 + 0x^2 + 15x - 20`.

To multiply the two polynomials
`(4x^3 + 0x^2 - 3x + 4)` and (2x - 5), we can use the distributive property. This property states that for any numbers a, b, and c:

(a + b) * c = a * c + b * c.

In this case, the first polynomial
`(4x^3 + 0x^2 - 3x + 4)` will be multiplied by each term of the second polynomial
`(2x - 5)`.

First, we multiply each term of the first polynomial by the first term of the second polynomial, which is 2x:

`(4x^3 + 0x^2 - 3x + 4)` *
`2x` =
`(4x^3 * 2x)` +
`(0x^2 * 2x)` +
`(-3x * 2x)` +
`(4 * 2x)`.

This simplifies to:

`8x^4 + 0x^3 - 6x^2 + 8x`.

Next, we multiply each term of the first polynomial by the second term of the second polynomial, which is -5:

`(4x^3 + 0x^2 - 3x + 4)` * -5 =
`(4x^3 * -5)` +
`(0x^2 * -5)` +
`(-3x * -5)` +
`(4 * -5).`

This simplifies to:

`-20x^3 + 0x^2 + 15x - 20.`

Finally, we add the results of these two multiplications together:

`(8x^4 + 0x^3 - 6x^2 + 8x) + (-20x^3 + 0x^2 + 15x - 20).`

Combining like terms gives us the final result:

`-20x^3 + 0x^2 + 15x - 20.`

So the multiplication of
`(4x^3 + 0x^2 - 3x + 4)` and
`(2x - 5)`results in
`-20x^3 + 0x^2 + 15x - 20.`