How do you divide $(2 v^{3} - 20 v^{2} + 56 v - 46) \div (v - 6)$ $(2v^3-20v^2+56v-46)div(v-6)$ using synthetic division?

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How do you divide $(2 v^{3} - 20 v^{2} + 56 v - 46) \div (v - 6)$ $(2v^3-20v^2+56v-46)div(v-6)$ using synthetic division?

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Answer 1 · 2017-06-11T13:05:00

The remainder is $= 2$ $=2$ and the quotient is $= 2 v^{2} - 8 v + 8$ $=2v^2-8v+8$

Explanation:

Let's perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $6$ $6$ $a a a a a$ $color(white)(aaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $2$ $2$ $a a a a a a$ $color(white)(aaaaaa)$ $- 20$ $-20$ $a a a a a a$ $color(white)(aaaaaa)$ $56$ $56$ $a a a a a$ $color(white)(aaaaa)$ $- 46$ $-46$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ _________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $a a a a a a a a$ $color(white)(aaaaaaaa)$ $12$ $12$ $a a a a$ $color(white)(aaaa)$ $- 48$ $-48$ $a a a a a a a$ $color(white)(aaaaaaa)$ $48$ $48$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ ________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $2$ $2$ $a a a a a a$ $color(white)(aaaaaa)$ $- 8$ $-8$ $a a a a a a a$ $color(white)(aaaaaaa)$ $8$ $8$ $a a a a a a a a$ $color(white)(aaaaaaaa)$ $2$ $color(red)(2)$

The remainder is $= 2$ $=2$ and the quotient is $= 2 v^{2} - 8 v + 8$ $=2v^2-8v+8$

$\frac{2 v^{3} - 20 v^{2} + 56 v - 46}{v - 6} = 2 v^{2} - 8 v + 8 + \frac{2}{v - 6}$ $(2v^3-20v^2+56v-46)/(v-6)=2v^2-8v+8+2/(v-6)$

Answer 2 · 2017-06-11T13:18:01

$2 v^{2} - 8 v + 8 remainder 2$ $2v^2 -8v+8 " remainder " 2$

Or $2 v^{2} - 8 v + 8 + \frac{2}{v - 6}$ $" "2v^2 -8v+8 + 2/(v-6)$

Explanation:

In synthetic division, you use only the coefficients, making sure that all powers of $v$ $v$ are considered:

$2 v^{3} - 20 v^{2} + 56 v^{1} - 46 v^{0}$ $color(red)(2)v^3 color(red)(-20)v^2 color(red)(+56)v^1 color(red)(-46)v^0$

Make $v - 6 = 0 \to v = 6 \leftarrow$ $v-6=0" "rarr v = color(blue)(6)" "larr$ this is written 'outside'.

$\times x . x ∣ 2 - 20 + 56 - 46$ $color(white)(xxx.x)|color(red)(2) " "color(red)(-20)" " color(red)(+56)" " color(red)(-46)$
$\times . \times ∣ ⏐ ↓$ $color(white)(xx.xx)|darr$
$color(white)(xx.x)color(blue)(6)|ul(color(white)(xxxxx)12" "-48" "48$
$color(white)(xxxxxx)color(red)(2)" "-8" "+8" "2larr$ the remainder

Steps are as follows:

Bring down the $color(red)(2)$

Multiply $color(blue)(6) xx color(red)(2) = 12$

Add $-20+12 = -8$

Multiply $color(blue)(6) xx -8 = -48$

Add $+56-48 = +8$

Multiply $color(blue)(6) xx 8 =48$

Add $-46+48 =+2$

What do the numbers tell us?

$2v^3div v= 2v^2" "larr$ this is the first term in the quotient.

The numbers represent the co-efficients of the following terms:

$" "color(red)(2)" "-8" "+8" "2larr$ the remainder

$" "2v^2" "-8v" "+8" remainder" 2$

This is the quotient.

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How do you divide $(2 v^{3} - 20 v^{2} + 56 v - 46) \div (v - 6)$ $(2v^3-20v^2+56v-46)div(v-6)$ using synthetic division?

2 Answers

Explanation:

Explanation:

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How do you divide $(2 v^{3} - 20 v^{2} + 56 v - 46) \div (v - 6)$ $(2v^3-20v^2+56v-46)div(v-6)$ using synthetic division?