Question

Choose the product.

(3x 2 + 2x - 3)(x - 1)

3x 2 + 3x - 4
3x 3 - 5x 2 - 5x + 3
3x 3 - x 2 - 5x + 3
3x 3 + 5x 2 - 5x + 3

Answer 1

3x 3 - x 2 - 5x + 3

Explanation:

To find the products, multiply x by each element of the longer expression 3x 2 + 2x - 3.

Then multiply each element of the longer expression again by -1 and add the results of the two products.

(3x 2 + 2x - 3)(x - 1)

= 3x^3 + 2x^2 - 3x - 3x^2 - 2x +3

Rearrange

= 3x^3 + 2x^2 - 3x^2 - 3x - 2x +3

simplify

= 3x^3 - x^2 - 5x + 3

Answer 2

`3 {x}^(3) - {x}^(2) - 5x + 3`

Explanation:

`( 3{x}^(2) + 2x - 3)(x - 1) \\ 3 {x}^(2) (x) + 2x(x) - 3(x) + 3{x}^(2) ( - 1) + 2x( - 1) - 3( - 1) \\ 3 {x}^(3) + 2 {x}^(2) - 3x - 3 {x}^(2) - 2x + 3 \\ 3{x}^(3) - {x}^(2) - 5x + 3`