Question

divide:~
6x⁵+4x⁴-3x³-1 by 3x²-x+1

step by step pls ​

Answer 1

Answer:

$2x^{3} +2x^{2} -x-1$

Step-by-step explanation:

Rewrite

$\\\frac{6x^{5}+4x^{4}-3x^{3} -1 }{3x^{2} -x+1}$

Factor the expressions

• $\frac{3x^{3}x(2x^{2} -1)+(2x^{2} -1)x(2x^{2} +1) }{3x^{2} -x+1}$

• $\frac{3x^{3} (\sqrt{2} x- 1)x (\sqrt{2}x+1)+(\sqrt{2}x-1)x(\sqrt{2} x+1)x(2x^{2} +1) }{3x^{2} -x+1}$

• $\frac{(\sqrt{2}x-1)x(\sqrt{2} x+1)x(3x^{3}+2x^{2} +1) }{3x^{2} -x+1}$

Rewrite the expression

$\frac{(\sqrt{2}x-1)x(\sqrt{2}x+1)x(3x^{3} +3x^{2} -x^{2} +1) }{3x^{2} -x+1}$

Rewrite and reorder

$\frac{(\sqrt{2}x-1)x(\sqrt{2}x+1)x(3x^{2} x(x+1)+1-x^{2} ) }{3x^{2} -x+1}$

Factor the expression

• $\frac{(\sqrt{2}x-1)x(\sqrt{2}x+1)x(3x^{2} x(x+1)+1-x^{2} }{3x^{2} -x+1}$

• $\frac{(\sqrt{2}x-1)x(\sqrt{2} x+1)x(x+1)x(3x^{2} +1-x) }{3x^{2} -x+1}$

Reduce the fraction

$(\sqrt{2}x-1)x(\sqrt{2} x+1)x(x+1)$

Simplify the product

$(2x^{2} -1)x(x+1)$

Remove the parentheses

$2x^{3} +2x^{2} -x-1$

Answer 2

Answer:

Rewrite

\begin{gathered}\\\frac{6x^{5}+4x^{4}-3x^{3} -1 }{3x^{2} -x+1}\end{gathered}

3x

2

−x+1

6x

5

+4x

4

−3x

3

−1

Factor the expressions

\frac{3x^{3}x(2x^{2} -1)+(2x^{2} -1)x(2x^{2} +1) }{3x^{2} -x+1}

3x

2

−x+1

3x

3

x(2x

2

−1)+(2x

2

−1)x(2x

2

+1)

\frac{3x^{3} (\sqrt{2} x- 1)x (\sqrt{2}x+1)+(\sqrt{2}x-1)x(\sqrt{2} x+1)x(2x^{2} +1) }{3x^{2} -x+1}

3x

2

−x+1

3x

3

(

2

x−1)x(

2

x+1)+(

2

x−1)x(

2

x+1)x(2x

2

+1)

\frac{(\sqrt{2}x-1)x(\sqrt{2} x+1)x(3x^{3}+2x^{2} +1) }{3x^{2} -x+1}

3x

2

−x+1

(

2

x−1)x(

2

x+1)x(3x

3

+2x

2

+1)

Rewrite the expression

\frac{(\sqrt{2}x-1)x(\sqrt{2}x+1)x(3x^{3} +3x^{2} -x^{2} +1) }{3x^{2} -x+1}

3x

2

−x+1

(

2

x−1)x(

2

x+1)x(3x

3

+3x

2

−x

2

+1)

Rewrite and reorder

\frac{(\sqrt{2}x-1)x(\sqrt{2}x+1)x(3x^{2} x(x+1)+1-x^{2} ) }{3x^{2} -x+1}

3x

2

−x+1

(

2

x−1)x(

2

x+1)x(3x

2

x(x+1)+1−x

2

)

Factor the expression

\frac{(\sqrt{2}x-1)x(\sqrt{2}x+1)x(3x^{2} x(x+1)+1-x^{2} }{3x^{2} -x+1}

3x

2

−x+1

(

2

x−1)x(

2

x+1)x(3x

2

x(x+1)+1−x

2

\frac{(\sqrt{2}x-1)x(\sqrt{2} x+1)x(x+1)x(3x^{2} +1-x) }{3x^{2} -x+1}

3x

2

−x+1

(

2

x−1)x(

2

x+1)x(x+1)x(3x

2

+1−x)

Reduce the fraction

(\sqrt{2}x-1)x(\sqrt{2} x+1)x(x+1)(

2

x−1)x(

2

x+1)x(x+1)

Simplify the product

(2x^{2} -1)x(x+1)(2x

2

−1)x(x+1)

Remove the parentheses

2x^{3} +2x^{2} -x-12x

3

+2x

2

−x−1