Question

17
drag the expressions to the correct locations on the image. not all expressions will be used.
consider this quotient.
$(x^3 - 8x + 6) \div (x^2 - 2x + 1)$
use long division to rewrite the quotient in an equivalent form as $q(x) + \frac{r(x)}{b(x)}$, where $q(x)$ is the quotient, $r(x)$ is the remainder, and $b(x)$ is the divisor.
$-11x + 12$
$-5x + 4$
$x^2 - 2x + 1$
$x - 6$
$x^3 - 8x + 6$
$x + 2$
$\square + \frac{\square}{\square}$
reset
next

Explanation:

Step1: Divide leading terms

$\frac{x^3}{x^2} = x$

Step2: Multiply divisor by $x$

$x(x^2 - 2x + 1) = x^3 - 2x^2 + x$

Step3: Subtract from dividend

$(x^3 - 8x + 6) - (x^3 - 2x^2 + x) = 2x^2 - 9x + 6$

Step4: Divide new leading terms

$\frac{2x^2}{x^2} = 2$

Step5: Multiply divisor by $2$

$2(x^2 - 2x + 1) = 2x^2 - 4x + 2$

Step6: Subtract to find remainder

$(2x^2 - 9x + 6) - (2x^2 - 4x + 2) = -5x + 4$

Step7: Write final form

$q(x) + \frac{r(x)}{b(x)}$, where $q(x)=x+2$, $r(x)=-5x+4$, $b(x)=x^2-2x+1$

Answer:

$x + 2 + \frac{-5x + 4}{x^2 - 2x + 1}$
(First blank: $x+2$; Numerator blank: $-5x+4$; Denominator blank: $x^2-2x+1$)