How do you use polynomial synthetic division to divide $(2 x^{3} + x^{2} + 2 x + 1) \div (x + \frac{1}{2})$ $(2x^3+x^2+2x+1)div(x+1/2)$ and write the polynomial in the form $p (x) = d (x) q (x) + r (x)$ $p(x)=d(x)q(x)+r(x)$ ?

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How do you use polynomial synthetic division to divide $(2 x^{3} + x^{2} + 2 x + 1) \div (x + \frac{1}{2})$ $(2x^3+x^2+2x+1)div(x+1/2)$ and write the polynomial in the form $p (x) = d (x) q (x) + r (x)$ $p(x)=d(x)q(x)+r(x)$ ?

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Answer 1 · 2017-08-07T19:08:46

The answer is $= (2 x^{2} + 2) (x + \frac{1}{2})$ $=(2x^2+2)(x+1/2)$

Explanation:

Let's perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $- \frac{1}{2}$ $-1/2$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $a a$ $color(white)(aa)$ $2$ $2$ $a a a a a a a$ $color(white)(aaaaaaa)$ $1$ $1$ $a a a a a a$ $color(white)(aaaaaa)$ $2$ $2$ $a a a a a a a$ $color(white)(aaaaaaa)$ $1$ $1$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ $- - - - - - - - - - - -$ $------------$

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $a a a a a$ $color(white)(aaaaa)$ $- 1$ $-1$ $a a a a a a$ $color(white)(aaaaaa)$ $0$ $0$ $a a a a a$ $color(white)(aaaaa)$ $- 1$ $-1$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ $- - - - - - - - - - - -$ $------------$

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a$ $color(white)(aaa)$ $2$ $2$ $a a a a a a a$ $color(white)(aaaaaaa)$ $0$ $0$ $a a a a a a$ $color(white)(aaaaaa)$ $2$ $2$ $a a a a a a$ $color(white)(aaaaaa)$ $0$ $color(red)(0)$

The remainder is $0$ $color(red)(0)$ and the quotient is $= 2 x^{2} + 2$ $=2x^2+2$

Therefore,

$(2 x^{3} + x^{2} + 2 x + 1) = (2 x^{2} + 2) (x + \frac{1}{2})$ $(2x^3+x^2+2x+1)=(2x^2+2)(x+1/2)$

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How do you use polynomial synthetic division to divide $(2 x^{3} + x^{2} + 2 x + 1) \div (x + \frac{1}{2})$ $(2x^3+x^2+2x+1)div(x+1/2)$ and write the polynomial in the form $p (x) = d (x) q (x) + r (x)$ $p(x)=d(x)q(x)+r(x)$ ?

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Explanation:

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How do you use polynomial synthetic division to divide (2x3+x2+2x+1)÷(x+12)(2x^3+x^2+2x+1)div(x+1/2) and write the polynomial in the form p(x)=d(x)q(x)+r(x)p(x)=d(x)q(x)+r(x)?

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Explanation:

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How do you use polynomial synthetic division to divide $(2 x^{3} + x^{2} + 2 x + 1) \div (x + \frac{1}{2})$ $(2x^3+x^2+2x+1)div(x+1/2)$ and write the polynomial in the form $p (x) = d (x) q (x) + r (x)$ $p(x)=d(x)q(x)+r(x)$ ?