the quotient of (x5 – 3x3 – 3x2 – 10x 15) and a polynomial is (x2 – 5). what is the polynomial?

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Edufirst Edufirst · Answer 1 · 2016-07-17T16:56:02+02:00

x^3 + 2x - 3

Just divide x^5-3x^3-3x^2-10x+15 by the quotient and you get the polynomial searched.

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lisboa lisboa · Answer 2 · 2019-06-17T19:23:53+02:00

Answer:

[tex]x^3+2x-3[/tex]

Step-by-step explanation:

the quotient of [tex](x^5 - 3x^3 - 3x^2 - 10x+15)[/tex]and a polynomial is [tex](x^2 -5)[/tex]

[tex]\frac{x^5 - 3x^3 - 3x^2 - 10x+15}{x^2-5}[/tex]

WE use long division

[tex]x^3+2x-3[/tex]

-------------------------------------------------

[tex](x^2-5)[/tex] [tex]x^5 - 0x^4-3x^3 - 3x^2 - 10x+15[/tex]

[tex]x^5 +0x^4 -5x^3[/tex]

--------------------------------------------------(subtract)

[tex]2x^3 - 3x^2-10x[/tex]

[tex]2x^3 + 0x^2 -10x[/tex]

------------------------------------------------------(subtract)

[tex]-3x^2+0x+15[/tex]

[tex]-3x^2+ 0x +15[/tex]

-----------------------------------------------------(subtract)

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