Question

Express the product of 2x squared plus 6x -8 and x+3 in standard form

Answer 1

The standard form is:

`2 {x}^(3) + 12 {x}^(2) + 10x - 24`

Step-by-step explanation

The given product is

`(2 {x}^(2) + 6x - 8)(x + 3)`

We expand using the distributive property to get:

`x(2 {x}^(2) + 6x - 8) + 3(2 {x}^(2) + 6x - 8)`

Expand the parenthesis;

`2 {x}^(3) + 6 {x}^(2) - 8x + 6 {x}^(2) + 18x - 24`

This simplifies to

`2 {x}^(3) + 12 {x}^(2) + 10x -24`

Standard form is when the polynomial is arranged in decreasing powers of x.