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General Polynomial Multiplication (page 3 of 3) Sections: Simple multiplication, "FOIL" (and a warning), General multiplication Sometimes you will have to multiply one multiterm polynomial by another multiterm polynomial. You can do this horizontally if you want, but there is so much room for error that I usually switch over to vertical multiplication once the polynomials get big. For bigger multiplications, vertical is usually faster, and is much more likely to give you a correct answer.
Here's what it looks like when done horizontally: (4x^{2}
– 4x
– 7)(x
+ 3)
Painful, no? Now I'll do it vertically: Much nicer! But, either way, the answer is: 4x^{3} + 8x^{2} – 19x – 21
I'm just going to do this one vertically. Note that, since order doesn't matter for multiplication, you can still put the "x + 2" polynomial on the bottom for vertical multiplication, just as you always put the smaller number on the bottom when you were doing regular vertical multiplication with just plain numbers. So the answer is: x^{4} + 5x^{3} + 10x^{2} – 9x – 34
I'll take my time, and do my work neatly: Copyright © Elizabeth Stapel 20002011 All Rights Reserved So the answer is: 6x^{4} – 6x^{3} – 47x^{2} + 83x – 35
Notice that these polynomials have "gaps" in their terms. The first polynomial has an x^{3} term, an x^{2} term, and a constant term, but no x term; and the second polynomial has an x^{3} term, an x term, and a constant term, but no x^{2} term. When I do the vertical multiplication, I will need to leave spaces in my setup, corresponding to the "gaps" in the degrees of the polynomials' terms, because I will almost certainly need the space. (This is similar to using zeroes as "place holders" in regular numbers. You might have a thousands digit of 3, a hundreds digit of 2, and a units digit of 5, so you'd put a 0 in for the tens digits, creating the number 3,205.) Here's what I mean: See how I needed the gaps? See how it helped that I had everything lined up according to the degree? If I hadn't left gaps, my terms could easily have become misaligned. Warning: Take the care to write things neatly, and you'll save yourself from many needless difficulties. The answer is: 2x^{6} + 4x^{5} + x^{4} + 11x^{3} + 2x^{2} + 4x + 4 << Previous Top  1  2  3  Return to Index


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