Algebra - Polynomials

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Section 1.4 : Polynomials

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9. Perform the indicated operation and identify the degree of the result.

\[\left( {{x^2} + x - 2} \right)\left( {3{x^2} - 8x - 7} \right)\]

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Start Solution

Remember that the foil method only works for binomials and these are both trinomials (i.e. they each have three terms).

So, all we need to do is multiply each term in the second polynomial by each term in the first polynomial. Here is the result of doing that.

\[\begin{align*}\left( {{x^2} + x - 2} \right)\left( {3{x^2} - 8x - 7} \right) & = 3{x^4} - 8{x^3} - 7{x^2} + 3{x^3} - 8{x^2} - 7x - 6{x^2} + 16x + 14\\ & = \require{bbox} \bbox[2pt,border:1px solid black]{{3{x^4} - 5{x^3} - 21{x^2} + 9x + 14}}\end{align*}\] Show Step 2

Remember the degree of a polynomial is just the largest exponent in the polynomial and so the degree of the result of this operation is four.