Question 92844
remember long division? ... you can use the same technique with polynomials


372 is the same as 3(10^2)+7(10)+2 ... just like 3x^2+7x+2


so, dividing x+3 into x^3+5x^2-6x+10 ... x goes into x^3, x^2 times ... (x^2)(x+3) is x^3+3x^2


(x^3+5x^2-6x+10)-(x^3+3x^2) is 2x^2-6x+10 ... x goes into 2x^2, 2x times ... (2x)(x+3) is 2x^2+6x


(2x^2-6x+10)-(2x^2+6x) is -12x+10 ... x goes into 12x+10, -12 times ... (-12)(x+3) is -12x-36


(12x+10)-(-12x-36) is 46 ... this is the remainder (it is not divisible by x)


this is done like long division ... with all the same power terms lined up vertically


not the case here, but if you were missing a term; like x^3+x-7 (no x^2 term); you would put in a zero for a place holder x^3+0x^2+x-7 ... to keep things properly aligned