Find a if the remainder is constant when 10x3−7x2+ax+6 is divided by 2x2−3x+1.
Solution — click to reveal
We perform the polynomial division: \multicolumn2r5x\cline2−52x2−3x+1\multicolumn2r−10x3\cline2−4\multicolumn2r0\multicolumn2r\cline3−5\multicolumn2r+410x3+15x28x2−8x20−7x2−5x(a−5)x+12x(a−5+12)x+ax6−42+6The remainder will be constant if and only if a−5+12=0. So a=−7.