How do you find f(3) given $f (x) = x^{3} - 7 x^{2} + 5 x - 6$ $f(x)=x^3-7x^2+5x-6$ using synthetic division?

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How do you find f(3) given $f (x) = x^{3} - 7 x^{2} + 5 x - 6$ $f(x)=x^3-7x^2+5x-6$ using synthetic division?

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Answer 1 · 2018-07-03T13:57:07

The remainder is $- 27$ $-27$ and the quotient is $= x^{2} - 4 x - 7$ $=x^2-4x-7$

Explanation:

Let's perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $3$ $3$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $- 7$ $-7$ $a a a a a a$ $color(white)(aaaaaa)$ $5$ $5$ $a a a a a a$ $color(white)(aaaaaa)$ $- 6$ $-6$

$a a a a a$ $color(white)(aaaaa)$ #|color(white)(aaaa)##color(white)(aaaaaa)3# $a a a a a$ $color(white)(aaaaa)$ $- 12$ $-12$ $a a a a$ $color(white)(aaaa)$ $- 21$ $-21$

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

$a a a a a$ $color(white)(aaaaa)$ #|color(white)(aaaa)# $1$ $1$ $a a a a$ $color(white)(aaaa)$ $- 4$ $-4$ $a a a a a a$ $color(white)(aaaaaa)$ $- 7$ $-7$ $a a a a a a$ $color(white)(aaaaaa)$ $- 27$ $color(red)(-27)$

The remainder is $- 27$ $-27$ and the quotient is $= x^{2} - 4 x - 7$ $=x^2-4x-7$

Therefore,

$\frac{x^{3} - 7 x^{2} + 5 x - 6}{x - 3} = (x^{2} - 4 x - 7) - \frac{27}{x - 3}$ $(x^3-7x^2+5x-6)/(x-3)=(x^2-4x-7)-27/(x-3)$

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How do you find f(3) given $f (x) = x^{3} - 7 x^{2} + 5 x - 6$ $f(x)=x^3-7x^2+5x-6$ using synthetic division?

1 Answer

Explanation:

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Impact of this question

Science

Math

Humanities

... and beyond

How do you find f(3) given f(x)=x3−7x2+5x−6f(x)=x^3-7x^2+5x-6 using synthetic division?

1 Answer

Explanation:

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How do you find f(3) given $f (x) = x^{3} - 7 x^{2} + 5 x - 6$ $f(x)=x^3-7x^2+5x-6$ using synthetic division?