Question

16. Divide using synthetic division,(x4 – xo - 38x? - 31x +45)-(x+5)x - 6x? - 8x + 9x - 8x' +9X-6x - x + 11x - 49x + 11x? - 22x - 49

Answer 1

We have to divide the polynomial using synthetic division.

We then have to write the coefficients as:

-5 _| 1 -1 -38 -31 45

-5 30 40 -45

____________________

1 -6 -8 9 0

Then, we have the coefficients of a polynomial with one degree less than the dividend.

As our dividend is degree 4, our result is grade 3 and the coefficients 1, -6, -8, 9 and 0 correspond to a 3rd degree polynomial and the remainder:

`(x^4-x^3-38x^2-31x+45)/\mleft(x+5\mright)=x^3-6x^2-8x+9+(0)/(x+5)`

In this case, the remainder is 0, as the ast coefficient is 0.

Answer: x^3-6x^2-8x+9 [First option]