Here are the solutions to the polynomial division problems.
- Divide x3−2x2−5x+6 by x−1.
Step 1: Perform polynomial long division.
\multicolumn2rx2\cline2−5x−1\multicolumn2r−(x3\cline2−3\multicolumn2r0\multicolumn2r\cline3−4\multicolumn2r\multicolumn2r\cline4−5\multicolumn2r−xx3−x2)−x2−(−x20−6−2x2−5x+x)−6x−(−6x0−5x+6+6)0+6
The quotient is x2−x−6.
- Divide 6x2−13x+5 by 2x−1.
Step 1: Perform polynomial long division.
\multicolumn2r3x\cline2−42x−1\multicolumn2r−(6x2\cline2−3\multicolumn2r0\multicolumn2r\cline3−4\multicolumn2r−56x2−3x)−10x−(−10x0−13x+5+5)0+5
The quotient is 3x−5.
- Find the quotient when x3+x2−x−1 is divided by x−1.
Step 1: Perform polynomial long division.
\multicolumn2rx2\cline2−5x−1\multicolumn2r−(x3\cline2−3\multicolumn2r0\multicolumn2r\cline3−4\multicolumn2r\multicolumn2r\cline4−5\multicolumn2r+2xx3−x2)2x2−(2x20+1+x2−x−2x)x−(x0−x−1−1)0−1
The quotient is x2+2x+1.
3 done, 2 left today. You're making progress.
