find the quotient

Question

Find the quotient and remainder for The quotient is ___The remainder is ___

Answer 1

The best strategy for polynomial division is to try to match your divisor to the highest power x in the dividend until it is no longer possible. In this case, the highest power in the dividend is x³. To match x³, multiply the divisor by x².

(x+4) * x² = x³+4x²

Now, write x² off to the side and subtract the term above (x³+4x²) from your dividend.

(x³+6x²+11x+7) - (x³+4x²) = 2x²+11x+7

Next, we repeat the process; match the divisor to the new dividend. In this case, we are trying to match x to 2x², so we should multiply the divisor by 2x

(x+4) * 2x = 2x²+8x

And subtract:

(2x²+11x+7) - (2x²+8x) = 3x + 7

Repeat the process once more, but don't forget what we multiplied the divisor by earlier. So far we have x² and 2x.

To match x+4 to 3x+7, we should multiply by 3.

(x+4) * 3 = 3x + 12

(3x + 7) - (3x+12) = -5

At this point, we can go no further. There is no way to subtract x + 4 from -5. Thus, -5 is our remainder. Our quotient is determined by the sum of all the terms we multiplied the divisor by to match the dividend. In total, our quotient is x²+2x+3.

Thus,

Quotient: x²+2x+3

Remainder: -5