How do you evaluate $f(x)=-4x^3+3x-5$ at x=2 using direct substitution and synthetic division?

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Answer 1 · 2018-07-21T12:27:23

The remainder is $-31$ and the quotient is $=-4x^2-8x-13$

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$color(white)(aaaaa)$ $|$ $color(white)(aaaa)$ $color(white)(aaaaaa)$ $-8$ $color(white)(aaaa)$ $-16$ $color(white)(aaaaa)$ $-26$

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$color(white)(aaaaa)$ $|$ $color(white)(aaaa)$ $-4$ $color(white)(aaaa)$ $-8$ $color(white)(aaaa)$ $-13$ $color(white)(aaaaa)$ $color(red)(-31)$

The remainder is $-31$ and the quotient is $=-4x^2-8x-13$

$(-4x^3+3x-5)/(x-2)=-4x^2-8x-13-31/(x-2)$

Apply the remainder theorem

When a polynomial $f(x)$ is divided by $(x-c)$ , we get

$f(x)=(x-c)q(x)+r$

Let $x=c$

Then,

$f(c)=0+r$

Here,

$f(x)=-4x^3+3x-5$

Therefore,

$f(2)=-4*2^3+3*2-5$

$=-32+6-5$

$=-31$

How do you evaluate f(x)=-4x^3+3x-5f(x)=-4x^3+3x-5 at x=2 using direct substitution and synthetic division?