Question

Using synthetic division for the following problem, what number would go in the divisor box? * (5x6 + 10x4 + 17x3 + 34x2 + 75x+150) + (x - 2) 02 O 5

Answer 1

2

1) Given that we're told to divide it using synthetic division, let's divide that polynomial

`5x^6+10x^4+17x^3+34x^2+75x+150\text{ by }(x-2)`

2) Enlisting the coefficients:

5 10 17 34 75 150

Let's try 2 as the zero, since

(x-2) =0

x-2 =0

x=2

2.2) Let's fill in the grid, by writing the coefficients orderly. Note that we don't have an x^5 term, so we'll write 0 instead. On the left upper place, we'll write the zero x=2, or simply 2.

Then we'll bring it down the highest coefficient.

We'll multiply 5, and then 10, by each number on the 1st row

So the answer to the question is 2, since the divisor box must be filled by the zero of this equation (x-2), x-2=0, x=2.