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# algebra

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If x^5 + 2x^3 + ax^2 + b is divisible by x^3 + 1, then find a and b.

May 19, 2020

#1
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If x^5 + 2x^3 + ax^2 + b is divisible by x^3 + 1, then find a and b.

Hello Guest!

$$\large \frac{x^5+2x^3+ax^2+b}{x^3+1}$$

$$(x^5+2x^3+ax^2+b):(x^3+1)=x^2+2$$

$$\underline{x^5}$$               $$\underline{+\ x^2}$$

$$2x^3$$     - -     $$+\ b$$

$$\underline{2x^3}$$             $$\underline{+\ 2}$$

- -                  - -

$$ax^2-x^2=0$$          $$b-2=0$$

a = 1                    b = 2

!

asinus

May 19, 2020