How do you simplify and divide $\frac{y^{3} + 3 y^{2} - 5 y - 4}{y + 4}$ $(y^3+3y^2-5y-4)/(y+4)$ ?

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How do you simplify and divide $\frac{y^{3} + 3 y^{2} - 5 y - 4}{y + 4}$ $(y^3+3y^2-5y-4)/(y+4)$ ?

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Answer 1 · 2017-07-05T09:35:08

The quotient is $= y^{2} - y - 1$ $=y^2-y-1$

Explanation:

Let's perform the synthetic division

$a a a a$ $color(white)(aaaa)$ $- 4$ $-4$ $a a a a$ $color(white)(aaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $1$ $1$ $a a a a$ $color(white)(aaaa)$ $3$ $3$ $a a a a a$ $color(white)(aaaaa)$ $- 5$ $-5$ $a a a a$ $color(white)(aaaa)$ $- 4$ $-4$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ _________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a a$ $color(white)(aaaa)$ $a a a$ $color(white)(aaa)$ $- 4$ $-4$ $a a a a a a$ $color(white)(aaaaaa)$ $4$ $4$ $a a a a a a$ $color(white)(aaaaaa)$ $4$ $4$
$a a a a a a a a a a a a$ $color(white)(aaaaaaaaaaaa)$ ________

$a a a a$ $color(white)(aaaa)$ $a a a a a a a$ $color(white)(aaaaaaa)$ $∣$ $|$ $a a a$ $color(white)(aaa)$ $1$ $1$ $a a a$ $color(white)(aaa)$ $- 1$ $-1$ $a a a a a$ $color(white)(aaaaa)$ $- 1$ $-1$ $a a a a a a$ $color(white)(aaaaaa)$ $0$ $color(red)(0)$

The remainder is $0$ $0$ and the quotient is $= y^{2} - y - 1$ $=y^2-y-1$

$\frac{y^{3} + 3 y^{2} - 5 y - 4}{y + 4} = y^{2} - y - 1$ $(y^3+3y^2-5y-4)/(y+4)=y^2-y-1$

Answer 2 · 2017-07-05T10:05:32

$y^{2} - y - 1$ $y^2-y-1$

Explanation:

$one way is to use the divisor as a factor in the numerator$ $"one way is to use the divisor as a factor in the numerator"$

$consider the numerator$ $"consider the numerator"$

$y^{2} (y + 4) - 4 y^{2} + 3 y^{2} - 5 y - 4$ $color(red)(y^2)(y+4)color(magenta)(-4y^2)+3y^2-5y-4$

$= y^{2} (y + 4) - y (y + 4) + 4 y - 5 y - 4$ $=color(red)(y^2)(y+4)color(red)(-y)(y+4)color(magenta)(+4y)-5y-4$

$= y^{2} (y + 4) - y (y + 4) - 1 (y + 4) + 4 - 4$ $=color(red)(y^2)(y+4)color(red)(-y)(y+4)color(red)(-1)(y+4)color(magenta)(+4)-4$

$= y^{2} (y + 4) - y (y + 4) - 1 (y + 4) + 0$ $=color(red)(y^2)(y+4)color(red)(-y)(y+4)color(red)(-1)(y+4)+0$

$rArr(cancel((y+4))(color(red)(y^2-y-1)))/cancel((y+4))$

$=y^2-y-1larr" quotient"$

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How do you simplify and divide $\frac{y^{3} + 3 y^{2} - 5 y - 4}{y + 4}$ $(y^3+3y^2-5y-4)/(y+4)$ ?

2 Answers

Explanation:

Explanation:

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How do you simplify and divide (y^3+3y^2-5y-4)/(y+4)y3+3y2−5y−4y+4(y^3+3y^2-5y-4)/(y+4)?

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How do you simplify and divide $\frac{y^{3} + 3 y^{2} - 5 y - 4}{y + 4}$ $(y^3+3y^2-5y-4)/(y+4)$ ?