How do you use synthetic division to show that x=1/2 is a zero of $2 x^{3} - 15 x^{2} + 27 x - 10 = 0$ $2x^3-15x^2+27x-10=0$ ?

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How do you use synthetic division to show that x=1/2 is a zero of $2 x^{3} - 15 x^{2} + 27 x - 10 = 0$ $2x^3-15x^2+27x-10=0$ ?

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Answer 1 · 2018-07-12T16:11:35

Please see the explanation below

Explanation:

Let's perform the synthetic division

Divide by $\frac{1}{2}$ $1/2$

$a a a a$ $color(white)(aaaa)$ $\frac{1}{2}$ $1/2$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $2$ $2$ $a a a a$ $color(white)(aaaa)$ $- 15$ $-15$ $a a a a a a$ $color(white)(aaaaaa)$ $27$ $27$ $a a a a a a$ $color(white)(aaaaaa)$ $- 10$ $-10$

$a a a a a a$ $color(white)(aaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $1$ $1$ $a a a a a$ $color(white)(aaaaa)$ $- 7$ $-7$ $a a a a a a a a$ $color(white)(aaaaaaaa)$ $10$ $10$

$a a a a a a a a a$ $color(white)(aaaaaaaaa)$ _________________________________________________________##

$a a a a a a$ $color(white)(aaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $2$ $2$ $a a a a$ $color(white)(aaaa)$ $- 14$ $-14$ $a a a a a a$ $color(white)(aaaaaa)$ $20$ $20$ $a a a a a a a a$ $color(white)(aaaaaaaa)$ $0$ $color(red)(0)$

The remainder is $= (0)$ $=(0)$ and the quotient is $= (2 x^{2} - 14 x + 20)$ $=(2x^2-14x+20)$

As the remainder $= 0$ $=0$ , $x = \frac{1}{2}$ $x=1/2$ is a root of $2 x^{3} - 15 x^{2} + 27 x - 10$ $2x^3-15x^2+27x-10$

$2 x^{3} - 15 x^{2} + 27 x - 10 = (2 x^{2} - 14 x + 20) (x - \frac{1}{2})$ $2x^3-15x^2+27x-10=(2x^2-14x+20)(x-1/2)$

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How do you use synthetic division to show that x=1/2 is a zero of $2 x^{3} - 15 x^{2} + 27 x - 10 = 0$ $2x^3-15x^2+27x-10=0$ ?

1 Answer

Explanation:

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How do you use synthetic division to show that x=1/2 is a zero of 2x^3-15x^2+27x-10=02x3−15x2+27x−10=02x^3-15x^2+27x-10=0?

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Explanation:

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How do you use synthetic division to show that x=1/2 is a zero of $2 x^{3} - 15 x^{2} + 27 x - 10 = 0$ $2x^3-15x^2+27x-10=0$ ?