Question #c7b2b

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Question #c7b2b

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Answer 1 · 2017-03-12T19:52:57

The remainder is $= - 3$ $=-3$ and the quotient is $= 3 y^{2} - 7$ $=3y^2-7$

Explanation:

You can perform a long division

$a a a a$ $color(white)(aaaa)$ $15 y^{3} - 27 y^{2} - 35 y + 60$ $15y^3-27y^2-35y+60$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $5 y - 9$ $5y-9$

$a a a a$ $color(white)(aaaa)$ $15 y^{3} - 27 y^{2}$ $15y^3-27y^2$ $a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaa)$ $∣$ $|$ $3 y^{2} - 7$ $3y^2-7$

$a a a a a a a a$ $color(white)(aaaaaaaa)$ $0 - 0 - 35 y + 60$ $0-0-35y+60$

$a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaa)$ $- 35 y + 63$ $-35y+63$

$a a a a a a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaaaaaaa)$ $0 - 3$ $0-3$

The remainder is $= - 3$ $=-3$ and the quotient is $= 3 y^{2} - 7$ $=3y^2-7$

You can check by doing a multiplication

$15 y^{3} - 27 y^{2} - 35 y + 60 = (5 y - 9) (3 y^{2} - 7) - 3$ $15y^3-27y^2-35y+60=(5y-9)(3y^2-7)-3$

Answer 2 · 2017-03-12T20:29:49

$y^{2} + \frac{18}{5} y - \frac{13}{25} + \frac{1383}{125 y - 225}$ $y^2+18/5y-13/25+1383/(125y-225)$

Same as:

$y^{2} + \frac{18}{5} y - \frac{13}{25} + \frac{1383}{25 (5 y - 9)}$ $y^2+18/5y-13/25+1383/(25(5y-9))$

Explanation:

Given $(5 y^{3} - 27 y^{2} - 35 y + 60) \div (5 y - 9)$ $" "(5y^3-27y^2-35y+60)-:(5y-9)$

$5 y^{3} - 27 y^{2} - 35 y + 60$ $" "5y^3-27y^2-35y+60$
$color(magenta)(y^2)(5y-9)->" "ul(5y^3-9y^2) larr" Subtract"$
$" "0-18y^2-35y+60$
$color(magenta)(18/5y)(5y-9)->" "ul(color(white)(.)18y^2-162/5y) larr" Subtract"$
$" "0-color(white)(.)13/5y+60$
$color(magenta)(-13/25)(5y-9)->" "ul(-13/5y+117/25) larr" Subtract"$
$color(magenta)(" Remainder "->+1383/25)$
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

$color(magenta)(y^2+18/5y-13/25+(1383/25 -:(5y-9)))$

$y^2+18/5y-13/25+1383/(125y-225)$

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Question #c7b2b

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