Answer :

EXPLANATION:

Given;

We are given the polynomial below;

[tex]6x^3+27x-19x^2-15[/tex]

Required;

We are required to divide the polynomial by;

[tex]3x-5[/tex]

Step-by-step solution;

We shall apply the synthetic division method of dividing polynomials.

The first step would be to re-arrange the polynomial in standard form. This is shown below;

[tex]6x^3-19x^2+27x-15[/tex]

Next step, we list out the coefficients of the polynomial;

[tex]6,-19,27,-15[/tex]

Next step, we identify the zeros of the denominator;

[tex]\begin{gathered} 3x-5=0 \\ \\ 3x=5 \\ \\ x=\frac{5}{3} \end{gathered}[/tex]

We can now write down the question in synthetic division format;

Next step, we carry down the leading coefficient below the division symbol.

Next step, we multiply this value by the zero of the denominator that is, 5/3.

That gives us;

[tex]6\times\frac{5}{3}=10[/tex]

Now we write 10 right under the next coefficient and that is -19. We add both together (-19 + 10 = -9) and write the result below the division symbol. Next we multiply this too by the zero of the denominator and we have;

[tex]-9\times\frac{5}{3}=-15[/tex]

We write this too under the next coefficient and we have;

[tex]27-15=12[/tex]

We multiply this too by 5/3 and we have 20. Write this right under the next coefficient and add up and we now have;

[tex]-15+20=5[/tex]

The result we have come up with are the coefficients beneath the division symbol and that is;

[tex]6,-9,12,5[/tex]

The last number is the remainder and the result of the division carried out will be;

[tex]6x^2-9x+12\text{ }Rem\text{ }5[/tex]

This is otherwise written out as follows;

ANSWER:

[tex]6x^2-9x+12+\frac{5}{(3x-5)}[/tex]

Thanks for taking the time to read Perform the indicated operations on the following polynomials Divide 6x3 27x 19x2 15 by 3x 5. We hope the insights shared have been valuable and enhanced your understanding of the topic. Don�t hesitate to browse our website for more informative and engaging content!

Rewritten by : Barada