| Arithmetic And Polynomials of Varying Bases | |
| The application to the left allows
the exploration of the multiplication and division of polynomials and
the relating of these processes to clerical long multiplication and
division. The application allows the varying of the Base or Place Value.
Thereby you can explore changing (X's) in polynomials. Whole
number
arithmetic, the multiplication and divsion of variables can be
practiced. With these skills then the multiplication of polynomials, the
combining of terms, the division of polynomials and synthetic division
can be explored. When you click the enter button, two polynomials will be generated for horizontal and vertical multiplication. Note across the top of the application, counters that allow changing the number range, the top polynomial exponent/placevalue range and the bottom polynomial exponent/place value range. |
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| The number range will set how large a number can be
generated depending on the base. The exponent ranges will set the polynomial to a trinomial,
binomial or constant. In other words, these ranges will set the
placevalue to powers of some (x). After you click the application to
set focus, press the up or down arrow to set range change to increase or
decrease, then place cursor bar or cursor arrow over the number counter of
the range you want to change and left click. Once ranges are set,
you may repeatedly press the enter button until prefered polynomials are
generated. Use Input Box to change Base. Now you can change the number counters in the vertical multiplication columns to input products of the integers of the top and bottom polynomials as you would for long multiplication. In addition to left clicking on a counter you may press the asterisk (*) or multiplication symbol to more rapidly increase or decrease a value. You may change the sign on a counter by pressing the left arrow for negative and the right arrow for positive. Once you input these products in the vertical columns, you can practice inputing them in front of the correct variables along the horizontal line above the long division columns. After you finish inputing one or more rows of products, you may check them for correctness by clicking the button to the right of the row. Practice arithmetic with integers and explore exponents. Now practice adding the integers by inputing your sums in the counters below the summation line. Before you press the summary button to check your inputs, practice inputing them in front of the correct variables under the division bar, then check correctness. The summary numerals will adjust to reflect numerals consistent with the input base. At this point, you can practice the division of polynomials. Input above the division bar the quotient of the highest degree divisor and dividend as you would for long division. Then multiply the divisor by the quotient in the same placevalue sequence as for long division. Subtract, bring down and start all over again just as you do for long division. Below the long multiplication columns there is an array to practice synthetic division. To practice synthetic division you must change the bottom polynomial range to 1 and to insure a zero remainder, after pressing, enter press the linear factor button. Centered to the left of the array is a counter to input the divisor. See a brief description of synthetic division |
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