How do you evaluate $f (x) = 5 x^{3} + 4 x^{2} + 8 x + 1$ $f(x)=5x^3+4x^2+8x+1$ at x=2 using direct substitution and synthetic division?

Question

How do you evaluate $f (x) = 5 x^{3} + 4 x^{2} + 8 x + 1$ $f(x)=5x^3+4x^2+8x+1$ at x=2 using direct substitution and synthetic division?

1 Answer

Impact of this question

2285 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-30T06:20:11

$f (x) = f (2) = 73$ $f(x) = f(2) = color(red)(73)$

Synthetic Division :
Quotient $Q = 5 x^{2} + 14 x + 36$ $color(brown)(Q = 5x^2 + 14x + 36)$ , Remainder $R = \frac{73}{x - 2}$ $color(red)(R = 73 / (x-2)$

Explanation:

Using direct substitution:

$f (x) = f (2) = 5 \cdot (2^{3}) + 4 \cdot (2^{2}) + (8 \cdot 2) + 1 = 40 + 16 + 16 + 1 = 73$ $f(x) =color(red)( f(2)) = 5*(2^3) + 4 * (2^2) + (8 * 2) + 1 = 40 + 16 + 16 + 1 = color(red)(73)$

Synthetic Division :

$a a 2 a a ∣ a a a 5 a a a 4 a a a 8 a a a 1$ $color(white)(aa)2color(white)(aa)|color(white)(aaa)5color(white)(aaa)4color(white)(aaa)8color(white)(aaa)1$
$a a a a a a ∣ a ⏐ ↓ a a 10 a a 28 a a 72$ $color(white)(aaaaaa)|color(white)(a)darrcolor(white)(aa)10color(white)(aa)28color(white)(aa)72$
$a a a a a a - - - - - - - -$ $color(white)(aaaaaa)--------$
$a a a a a a a a a a 5 a a 14 a a 36 a a 73$ $color(white)(aaaaaaaaaa)5color(white)(aa)14color(white)(aa)36color(white)(aa)73$

Quotient $Q = 5 x^{2} + 14 x + 36$ $color(brown)(Q = 5x^2 + 14x + 36)$ , Remainder $R = \frac{73}{x - 2}$ $color(red)(R = 73 / (x-2)$

Science

Math

Humanities

... and beyond

How do you evaluate $f (x) = 5 x^{3} + 4 x^{2} + 8 x + 1$ $f(x)=5x^3+4x^2+8x+1$ 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)=5x3+4x2+8x+1f(x)=5x^3+4x^2+8x+1 at x=2 using direct substitution and synthetic division?

1 Answer

Explanation:

Related questions

Impact of this question

How do you evaluate $f (x) = 5 x^{3} + 4 x^{2} + 8 x + 1$ $f(x)=5x^3+4x^2+8x+1$ at x=2 using direct substitution and synthetic division?