Polynomial Multiplication
When you explore multiplication of polynomials consisting of trinomial expressions, the process does not vary from those of other types of polynomial multiplications, but they do become more involved. Here is a multiplication problem involving a binomial and a trinomial. You must multiply each term of the first expression by each term of the second expression.
| (x2 + 3x − 4)(2x2 + 3) | Trinomial and binomial. |
| x2(2x2 + 3)+ 3x(2x2 + 3) − 4(2x2 + 3) | Distribution. |
| x2(2x2) + x2(3) + 3x (2x2) + 3x (3) − 4(2x2) − 4(3) | Multiplying. |
| 2x4 + 3x2 + 6x3 + 9x − 8x2 − 12 | Collect terms. |
| 2x4 + 6x3 + 3x2 − 8x2 + 9x − 12 | Group like terms. |
| 2x4 + 6x3 − 5x2 + 9x + 8x − 12 | Simplify. |
When you deal with polynomials that consist of several terms, you can use approaches drawn from arithmetic. When you use such approaches, ordering the terms in a polynomial by degree constitutes an important step. You can then arrange the expressions in columns and carry out the multiplications. Here is an example involving a trinomial and a binomial:
Exercise Set 8.3Solve each equation. |
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