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

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Answer 1 · 2018-07-03T13:57:07

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

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

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

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

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

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

Therefore,

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

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