Question

BRAINLIESTTT ASAP! PLEASE HELP ME :)

Answer 1

Answer:

$\large \boxed{2x^{2} - x + 1}$

Explanation:

Let's try both methods.

1. Long division

                2x² - x + 1

x + 1)2x³ +   x²       + 1

       2x³ + 2x²

                  -x²

                  -x² - x

                          x + 1

                          x + 1

                               0

$\text{The quotient is \large \boxed{\mathbf{2x^{2} - x + 1}} }$

2. Synthetic division

$\begin{array}{r|rrrr}-1& 2 & 1 & 0 & 1\\ & & -2& 1 & -1\\ & 2 & -1& 1 & 0\\\end{array}$

Thus,

$\dfrac{2x^{3} + x^2 + 1} {x +1} = 2x^{2} - x + 1\\\\\text{The quotient is \large \boxed{\mathbf{2x^{2} - x + 1}} }$

Answer 2

Answer:

$\displaystyle \boxed{2x^2 - x + 1}$

Step-by-step explanation:

Since the divisor of $\displaystyle x + 1$is in the form of $\displaystyle x - c,$use what is called Synthetic Division. Remember, in this formula, −c gives you the OPPOSITE terms of what they really are, so do not forget it. Anyway, here is how it is done:

−1| 2 1 0 1

↓ −2 1 −1

__________

2 −1 1 0 → $\displaystyle 2x^2 - x + 1$

You start by placing the c in the top left corner, then list all the coefficients of your dividend [2x³ + x² + 1]. You bring down the original term closest to c then begin your multiplication. Now depending on what symbol your result is tells you whether the next step is to subtract or add, then you continue this process starting with multiplication all the way up until you reach the end. Now, when the last term is 0, that means you have no remainder. Finally, your quotient is one degree less than the leading coefficient of your dividend, so that 2 in your quotient can be a 2x², the −x follows right behind it, and bringing up the rear, 1, giving you the quotient of 2x² - x + 1.

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