How do you simplify and divide $(t^{5} - 3 t^{2} - 20) {(t - 2)}^{- 1}$ $(t^5-3t^2-20)(t-2)^-1$ ?

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How do you simplify and divide $(t^{5} - 3 t^{2} - 20) {(t - 2)}^{- 1}$ $(t^5-3t^2-20)(t-2)^-1$ ?

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Answer 1 · 2017-10-15T01:07:03

Quotient $t^{4} + 2 t^{3} + 8 t^{2} + 5 t + 10$ $t^4+2t^3+8t^2+5t+10$ , Remainder $= 0$ $=0$

Explanation:

$\frac{t^{5} - 3 t^{2} - 20}{t - 2}$ $(t^5-3t^2-20)/(t-2)$
We will follow synthetic division method.

$2 a a a ∣ a 1 a a a 0 a a a 0 a a a - 3 a a a 0 a a a - 20$ $2color(white)( aaa) |color(white)(a) 1 color(white)(aaa) 0 color(white)(aaa)0 color(white)(aaa)-3 color(white)(aaa) 0 color(white)(aaa) -20$
$a a a a ∣ a a a a a 2 a a a 4 a a a a a 8 a a a 10 a a a a a 20$ $color(white)(aaaa) | color(white)(aaaaa) 2 color(white)(aaa) 4 color(white)(aaaaa) 8 color(white)(aaa) 10 color(white)(aaaaa) 20$
$a a a a ∣ \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots \dots$ $color(white)(aaaa) | …………………………………$
$a a a a a a a 1 a a a 2 a a a 8 a a a a a 5 a a a 10 a a a a a a 0$ $color(white)( aaaaaaa) 1 color(white)(aaa) 2 color(white)(aaa) 8 color(white)(aaaaa) 5 color(white)(aaa) 10 color(white)(aaaaaa)0$

Quotient is $t^{4} + 2 t^{3} + 8 t^{2} + 5 t + 10$ $t^4+2t^3+8t^2+5t+10$ , Remainder #=0

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How do you simplify and divide $(t^{5} - 3 t^{2} - 20) {(t - 2)}^{- 1}$ $(t^5-3t^2-20)(t-2)^-1$ ?

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Explanation:

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How do you simplify and divide (t^5-3t^2-20)(t-2)^-1(t5−3t2−20)(t−2)−1(t^5-3t^2-20)(t-2)^-1?

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How do you simplify and divide $(t^{5} - 3 t^{2} - 20) {(t - 2)}^{- 1}$ $(t^5-3t^2-20)(t-2)^-1$ ?