Respuesta :
We need to find a polynomial in standard form. For this, we have:
Divisor (d):
[tex]Divisor(d)\Rightarrow x-3[/tex]Quotient (q):
[tex]\text{Quotient(q)}=2x^2-5x-5[/tex]Remainder (R):
[tex]R=9[/tex]Then, we know that if we have all of these "components", we can use them using the following formula:
[tex]D=d\cdot q+R[/tex]This is the formula to find the dividend of a division. Then, we have that the function f(x) will be:
[tex]D=(x-3)(2x^2-5x-5)+9_{}[/tex]To solve this, we need to multiply the binomial (x - 3) by the trinomial as follows:
1. The unknown variable x by any of the terms of the trinomial:
[tex]x(2x^2)+x(-5x)+x(-5)=2x^3-5x^2-5x[/tex]2. And we need the latter to the result of multiplying -3 by any of the terms of the trinomial:
[tex]-3(2x^2)-3(-5x)-3(-5)=-6x^2+15x+15[/tex]Now, we need to add both partial results as follows (we need to add like terms):
[tex]2x^3-5x^2-5x-6x^2+15x+15[/tex][tex]2x^3-5x^2-6x^2-5x+15x+15[/tex][tex]2x^3-11x^2+10x+15[/tex]And now, we need to add the remainder:
[tex]D=2x^3-11x^2+10x+15+9\Rightarrow D=2x^3-11x^2+10x+24[/tex]Therefore, the function is:
[tex]undefined[/tex]the dividend of a division. Then, we have
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