Question

(x2 - 5x +2) x (3x2 +2x +3)

Answer 1

3x^4 -13x^3 -x^2 - 11x + 6

Explanation:

(x^2 - 5x + 2) x (3x^2 + 2x + 3)

x^2 (3x^2 + 2x + 3) - 5x (3x^2 + 2x + 3) + 2 (3x^2 + 2x + 3)

3x^4 + 2x^3 + 3x^2 - 15x^3 -10x^2 -15x + 6x^2 +4x + 6

combine like terms

3x^4 -13x^3 -x^2 - 11x + 6

Answer 2

For this case we must find the product of the following expression:

`(x ^ 2-5x + 2) (3x ^ 2 + 2x + 3) =`

We must apply distributive property term by term, remembering the following power multiplication property of the same base:

`a ^ n * a ^ m = a ^ {n + m}`

We also take into account that:

`- * - = +\\- * + = -`

So:

`3x ^ 4 + 2x ^ 3 + 3x ^ 2-15x ^ 3-10x ^ 2-15x + 6x ^ 2 + 4x + 6 =`

Now we add similar terms taking into account that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed.

`3x ^ 4 + 2x ^ 3-15x ^ 3 + 3x ^ 2-10x ^ 2 + 6x ^ 2-15x + 4x + 6 =\\3x ^ 4-13x ^ 3-x ^ 2-11x + 6`

Answer:

`3x ^ 4-13x ^ 3-x ^ 2-11x + 6`