$4 x^{3} - 24 x^{2} + 29 x + 15 \div 2 x + 5$ $4x^3-24x^2+29x+15 -: 2x+5$ ?

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$4 x^{3} - 24 x^{2} + 29 x + 15 \div 2 x + 5$ $4x^3-24x^2+29x+15 -: 2x+5$ ?

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Answer 1 · 2017-02-06T20:33:37

$= 4 x^{3} - 24 x^{2} + 36 \frac{1}{2} x + 5$ $=4x^3-24x^2+36 1/2x+5$

$36 \frac{1}{2} x$ $36 1/2x$ can also be written as $36.5 x or \frac{73}{2} x$ $36.5x " or "73/2x$

Explanation:

$4 x^{3} - 24 x^{2} + 29 x + \frac{15}{2} x + 5$ $4x^3-24x^2+29x+15/2x+5$

As there is no indication of what is required, we might assume it is just simplify.

The only like terms are those in $x$ $x$ , which need to be added.

$= 4 x^{3} - 24 x^{2} + 29 x + 7 \frac{1}{2} x + 5$ $=4x^3-24x^2+29x+7 1/2x+5$

$= 4 x^{3} - 24 x^{2} + 36 \frac{1}{2} x + 5$ $=4x^3-24x^2+36 1/2x+5$

Answer 2 · 2017-02-06T21:13:54

$\frac{4 x^{3} - 24 x^{2} + 29 x + 15}{2 x + 5} = 2 x^{2} - 17 x + 57 - \frac{270}{2 x + 5}$ $(4x^3-24x^2+29x+15)/(2x+5) = 2x^2-17x+57-270/(2x+5)$

Explanation:

I think the question was intended to ask for the result of the division:

$\frac{4 x^{3} - 24 x^{2} + 29 x + 15}{2 x + 5}$ $(4x^3-24x^2+29x+15)/(2x+5)$

We can split the numerator into multiples of $(2 x + 5)$ $(2x+5)$ like this:

$4 x^{3} - 24 x^{2} + 29 x + 15 = (4 x^{3} + 10 x^{2}) - (34 x^{2} + 85 x) + (114 x + 285) - 270$ $4x^3-24x^2+29x+15 = (4x^3+10x^2)-(34x^2+85x)+(114x+285)-270$

$4 x^{3} - 24 x^{2} + 29 x + 15 = 2 x^{2} (2 x + 5) - 17 x (2 x + 5) + 57 (2 x + 5) - 270$ $color(white)(4x^3-24x^2+29x+15) = 2x^2(2x+5)-17x(2x+5)+57(2x+5)-270$

$4 x^{3} - 24 x^{2} + 29 x + 15 = (2 x^{2} - 17 x + 57) (2 x + 5) - 270$ $color(white)(4x^3-24x^2+29x+15) = (2x^2-17x+57)(2x+5)-270$

So:

$\frac{4 x^{3} - 24 x^{2} + 29 x + 15}{2 x + 5} = \frac{(2 x^{2} - 17 x + 57) (2 x + 5) - 270}{2 x + 5}$ $(4x^3-24x^2+29x+15)/(2x+5) = ((2x^2-17x+57)(2x+5)-270)/(2x+5)$

$\frac{4 x^{3} - 24 x^{2} + 29 x + 15}{2 x + 5} = (2 x^{2} - 17 x + 57) - \frac{270}{2 x + 5}$ $color(white)((4x^3-24x^2+29x+15)/(2x+5)) = (2x^2-17x+57)-270/(2x+5)$

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$4 x^{3} - 24 x^{2} + 29 x + 15 \div 2 x + 5$ $4x^3-24x^2+29x+15 -: 2x+5$ ?

2 Answers

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$4 x^{3} - 24 x^{2} + 29 x + 15 \div 2 x + 5$ $4x^3-24x^2+29x+15 -: 2x+5$ ?