Question

divide $(6x^3 - 5x^2 + 7x - 3)$ by $(2x - 1)$. what is the quotient. $3x^2 - x + 3$ $3x + 1 - \frac{3}{2x - 1}$ $3x - 1 + \frac{3}{2x - 1}$ $3x^2 + x - 3$ 2 multiple choice 20 points what is the quotient of: $(x^3 - 3x^2 + 3x - 1) \div (x + 1)$ $x^2 - 4x + 7 + \frac{8}{x + 1}$ $x^2 - 4x + 7$ $x^2 - 4x + 7 - \frac{8}{x + 1}$ $x^2 - 3x + 3$ clear my selection

Explanation:

Step1: Divide leading terms

$\frac{6x^3}{2x} = 3x^2$

Step2: Multiply divisor by $3x^2$

$3x^2(2x-1) = 6x^3 - 3x^2$

Step3: Subtract from dividend

$(6x^3-5x^2+7x-3)-(6x^3-3x^2) = -2x^2+7x-3$

Step4: Divide new leading terms

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

Step5: Multiply divisor by $-x$

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

Step6: Subtract from current polynomial

$(-2x^2+7x-3)-(-2x^2+x) = 6x-3$

Step7: Divide new leading terms

$\frac{6x}{2x} = 3$

Step8: Multiply divisor by 3

$3(2x-1) = 6x-3$

Step9: Subtract to find remainder

$(6x-3)-(6x-3) = 0$
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Step1: Divide leading terms

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

Step2: Multiply divisor by $x^2$

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

Step3: Subtract from dividend

$(x^3-3x^2+3x-1)-(x^3+x^2) = -4x^2+3x-1$

Step4: Divide new leading terms

$\frac{-4x^2}{x} = -4x$

Step5: Multiply divisor by $-4x$

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

Step6: Subtract from current polynomial

$(-4x^2+3x-1)-(-4x^2-4x) = 7x-1$

Step7: Divide new leading terms

$\frac{7x}{x} = 7$

Step8: Multiply divisor by 7

$7(x+1) = 7x+7$

Step9: Subtract to find remainder

$(7x-1)-(7x+7) = -8$

Answer:

1. $3x^2 - x + 3$
2. $x^2 - 4x + 7 - \frac{8}{x+1}$