How do you use synthetic division to divide $\frac{3 x^{3} - 4 x^{2} + 5}{x - \frac{3}{2}}$ $(3x^3-4x^2+5)/(x-3/2)$ ?

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How do you use synthetic division to divide $\frac{3 x^{3} - 4 x^{2} + 5}{x - \frac{3}{2}}$ $(3x^3-4x^2+5)/(x-3/2)$ ?

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Answer 1 · 2017-02-21T18:14:02

The remainder is $= \frac{49}{8}$ $=49/8$ and the quotient is $= 3 x^{2} + \frac{1}{2} x + \frac{3}{4}$ $=3x^2+1/2x+3/4$

Explanation:

We perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $\frac{3}{2}$ $3/2$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $3$ $3$ $a a a a$ $color(white)(aaaa)$ $- 4$ $-4$ $a a a a a$ $color(white)(aaaaa)$ $0$ $0$ $a a a a a a$ $color(white)(aaaaaa)$ $5$ $5$

$a a a a a a$ $color(white)(aaaaaa)$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $a a a$ $color(white)(aaa)$ $a a a a a a a a$ $color(white)(aaaaaaaa)$ $\frac{9}{2}$ $9/2$ $a a a a$ $color(white)(aaaa)$ $\frac{3}{4}$ $3/4$ $a a a a$ $color(white)(aaaa)$ $\frac{9}{8}$ $9/8$

$a a a a a a a a a a$ $color(white)(aaaaaaaaaa)$ ------------------------------------------------------------

$a a a a$ $color(white)(aaaa)$ $a a a a a a$ $color(white)(aaaaaa)$ $a a a a a a$ $color(white)(aaaaaa)$ $3$ $3$ $a a a a a$ $color(white)(aaaaa)$ $\frac{1}{2}$ $1/2$ $a a a a a$ $color(white)(aaaaa)$ $\frac{3}{4}$ $3/4$ $a a a a a$ $color(white)(aaaaa)$ $\frac{49}{8}$ $color(red)(49/8)$

The remainder is $= \frac{49}{8}$ $=49/8$

The quotient is $= 3 x^{2} + \frac{1}{2} x + \frac{3}{4}$ $=3x^2+1/2x+3/4$

Verification, by using the remainder theorem

$f (\frac{3}{2}) = \frac{81}{8} - 9 + 5 = \frac{81}{8} - 4 = \frac{49}{8}$ $f(3/2)=81/8-9+5=81/8-4=49/8$

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How do you use synthetic division to divide $\frac{3 x^{3} - 4 x^{2} + 5}{x - \frac{3}{2}}$ $(3x^3-4x^2+5)/(x-3/2)$ ?

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Explanation:

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How do you use synthetic division to divide $\frac{3 x^{3} - 4 x^{2} + 5}{x - \frac{3}{2}}$ $(3x^3-4x^2+5)/(x-3/2)$ ?