How do you use long division to divide $(6 x^{3} + 10 x^{2} + x + 8) \div (2 x^{2} + 1)$ $(6x^3+10x^2+x+8)div(2x^2+1)$ ?

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How do you use long division to divide $(6 x^{3} + 10 x^{2} + x + 8) \div (2 x^{2} + 1)$ $(6x^3+10x^2+x+8)div(2x^2+1)$ ?

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Answer 1 · 2017-05-17T15:24:34

The quotient is $= 3 x + 1$ $=3x+1$ and the remainder is $= - 2 x + 3$ $=-2x+3$

Explanation:

Let's perform the long division

$a a a a$ $color(white)(aaaa)$ $2 x^{2} + 1$ $2x^2+1$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $6 x^{3} + 10 x^{2} + x + 8$ $6x^3+10x^2+x+8$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $3 x + 5$ $3x+5$

$a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaa)$ $6 x^{3}$ $6x^3$ $a a a a a a a$ $color(white)(aa aaaaa)$ $+ 3 x$ $+3x$ $a a a a$ $color(white)(aaaa)$

$a a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaaa)$ $0$ $0$ $a a a a$ $color(white)(aa aa)$ $10 x^{2}$ $10x^2$ $- 2 x$ $-2x$ $a a a a$ $color(white)(aaaa)$

$a a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaaa)$ $a a a a a$ $color(white)(aa aaa)$ $10 x^{2}$ $10x^2$ $a a a a$ $color(white)(aaaa)$ $+ 5$ $+5$ $a a a a$ $color(white)(aaaa)$

$a a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaaa)$ $a a a a a a$ $color(white)(aa aaaa)$ $0$ $0$ $a a a a a a$ $color(white)(aaaaaa)$ $+ 3$ $+3$ $a a a a$ $color(white)(aaaa)$

$a a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaaa)$ $a a a a a a a a$ $color(white)(aa aaaaaa)$ $- 2 x$ $-2x$ $a a$ $color(white)(aa)$ $+ 3$ $+3$ $a a a a$ $color(white)(aaaa)$

$\frac{6 x^{3} + 10 x^{2} + x + 8}{2 x^{2} + 1} = (3 x + 5) + \frac{- 2 x + 3}{2 x^{2} + 1}$ $(6x^3+10x^2+x+8)/(2x^2+1)=(3x+5)+(-2x+3)/(2x^2+1)$

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How do you use long division to divide $(6 x^{3} + 10 x^{2} + x + 8) \div (2 x^{2} + 1)$ $(6x^3+10x^2+x+8)div(2x^2+1)$ ?

1 Answer

Explanation:

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How do you use long division to divide (6x^3+10x^2+x+8)div(2x^2+1)(6x3+10x2+x+8)÷(2x2+1)(6x^3+10x^2+x+8)div(2x^2+1)?

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Explanation:

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How do you use long division to divide $(6 x^{3} + 10 x^{2} + x + 8) \div (2 x^{2} + 1)$ $(6x^3+10x^2+x+8)div(2x^2+1)$ ?