Question

I REALLY NEED HELP!!!!

Answer 1

Divide x^4+x^3+7x^2-6x+8 by x+2+2x+8 using long polynomial division.

Answer:
x^2-x+1

Answer 2

Answer:

x²-x+1

Step-by-step explanation:

We write the dividend, x⁴+x³+7x²-6x+8, under the division box.  We write the divisor, x²+2x+8, outside the box to the left.

We see how many times x² goes into x⁴.  It will go x² times.  We write this on the line above the dividend.  We multiply back through;

x²(x²+2x+8) = x⁴+2x³+8x²

We write this under the first three terms of the dividend.  We then subtract:

(x⁴+x³+7x²)-(x⁴+2x³+8x²) = -1x³-1x²

This goes below the subtraction.  We bring down the next term, -6x.

Next we see how many times x² goes into -1x³.  It goes -x times; we write this beside the x² in the quotient.  We multiply back through:

-x(x²+2x+8) = -x³-2x²-8x

This goes below the -1x³-1x²-6x.  We subtract the two:

(-1x³-1x²-6x)-(-x³-2x²-8x) = -1x³+1x³-1x²+2x²-6x+8x = 1x²+2x

We write this below the last line in the work.  We bring down the last term, 8.

Now we see how many times x² goes into 1x².  It goes 1 time; since this is positive, we write +1 beside the answer we have at the top.  Multiply back through:

1(x²+2x+8) = x²+2x+8

Now we subtract:

(x²+2x+8)-(x²+2x+8) = 0

This makes our answer x²-x+1