How do you solve this polynomial:(3x + 1 )(x2 – 4x + 2)

Expert Answers
sciencesolve eNotes educator| Certified Educator

You need to perform multiplication of two polynomials, hence you need to multiply each term from first brackets to each term from the second brackets such that:

`(3x + 1 )(x^2 – 4x + 2) = 3x*x^2 + 3x*(-4x) + 3x*2 + 1*x^2 + 1*(-4x) + 1*2`

`(3x + 1 )(x^2 – 4x + 2) = 3x^3 - 12x^2 + 6x + x^2 - 4x + 2`

You need to add or subtract the coefficients of like powers such that:

`(3x + 1 )(x^2 – 4x + 2) = 3x^3 + x^2(-12 + 1) + x(6 - 4) + 2`

`(3x + 1 )(x^2 – 4x + 2) = 3x^3 - 11x^2 + 2x ` `+ 2`

Hence, performing the multiplication of polynomials yields `(3x + 1 )(x^2 – 4x + 2) = 3x^3 - 11x^2 + 2x + 2.`

nmmoritz eNotes educator| Certified Educator

Every term in the first binomial must be multiplied by every term in the trinomial.

Therefore, when multiplying 3x by every term in the second set of parentheses, you get:

3x^3 - 12x^2 + 6x

and multiplying 1 by every term in the second set of parentheses gives you:

x^2 - 4x + 2

Combine the two, and you get:

3x^3 - 12x^2 + 6x + x^2 - 4x + 2

Now, combine like terms and write your answer in descending order of the variable:

3x^3 - 11x^2 + 2x + 2