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

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sciencesolve | Teacher | (Level 3) Educator Emeritus

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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.`

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nmmoritz | Middle School Teacher | (Level 1) Adjunct Educator

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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

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