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

Question

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

1 Answer

Impact of this question

1827 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-07-21T12:27:23

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

Explanation:

Let's perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $2$ $2$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $- 4$ $-4$ $a a a a a$ $color(white)(aaaaa)$ $0$ $0$ $a a a a a a$ $color(white)(aaaaaa)$ $3$ $3$ $a a a a a a a$ $color(white)(aaaaaaa)$ $- 5$ $-5$

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

$a a a a a a a a a$ $color(white)(aaaaaaaaa)$ _________

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

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

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

Apply the remainder theorem

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

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

Let $x = c$ $x=c$

Then,

$f (c) = 0 + r$ $f(c)=0+r$

Here,

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

Therefore,

$f (2) = - 4 \cdot 2^{3} + 3 \cdot 2 - 5$ $f(2)=-4*2^3+3*2-5$

$= - 32 + 6 - 5$ $=-32+6-5$

$= - 31$ $=-31$

Science

Math

Humanities

... and beyond

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

1 Answer

Explanation:

Related questions

Impact of this question

Science

Math

Humanities

... and beyond

How do you evaluate f(x)=-4x^3+3x-5f(x)=−4x3+3x−5f(x)=-4x^3+3x-5 at x=2 using direct substitution and synthetic division?

1 Answer

Explanation:

Related questions

Impact of this question

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