Question

Hello, I want to know what is the product of the polynomial below
`(6 {x}^(2) - 3x - 6)(4 {x}^(2) + 5x + 4)`

Answer 1

GIVEN:

We are given the polynomials below;

`(6x^2-3x-6)(4x^2+5x+4)`

Required;

To determine the product of the polynomials given.

Step-by-step solution;

We shall multiply the terms in parenthesis by distributing the terms on the left among the ones on the right one after the other as shown below;

`\begin{gathered} 6x^2*(4x^2+5x+4) \\ \\ -3x*(4x^2+5x+4) \\ \\ -6*(4x^2+5x+4) \end{gathered}`

We can now simplify as follows;

`24x^4+30x^3+24x^2-12x^3-15x^2-12x-24x^2-30x-24`

Next step, we collect all like terms;

`\begin{gathered} 24x^4+30x^3-12x^3+24x^2-24x^2-15x^2-12x-30x-24 \\ \\ =24x^4+18x^3-15x^2-42x-24 \end{gathered}`

Therefore, the product of the polynomials

ANSWER:

`24x^4+18x^3-15x^2-42x-24`