The table represents the start of the division -2x^3+11x^2-23x+20 of by x^2-3x+4 . Which terms belong in one of the shaded cells in the table? Check all that apply.
SH= shaded
-2x 5
x^2 SH SH
-3x SH SH
4 SH SH
By polynomial grid division, we start by the divisor x²-3x+4 placed on the row headings of the table and end with the quotient -2x + 5 on the column headings as given. We know that -2x³ must be in the top left which means that the first column entry is indeed -2x. So the row and column multiply to -2x³. We use this to fill in all of the first column, multiplying -2x by the terms of the row entries. -2x 5 x² -2x³ -3x 6x² 4 -8x We now got 6x² though we want 11x². The next quadratic entry must then be 5x² so that the overall sum is 11x². Multiplying 5 by the terms of the row entries, we fill in all of the second column: -2x 5 x² -2x³ 5x² -3x 6x² -15x 4 -8x 20
The bottom and final term is 20, which is our desired answer and we can read the quotient off the first row: -2x³ +11x² - 23x + 20 / x² - 3x + 4 = -2x + 5 We have calculated for all the terms that belong in table, therefore, the terms 5x² and 6x² belong in the shaded cells.
