Answer:
[1.(x)²+ 8.(x) + 19] + [tex]\frac{39}{(x - 2)}[/tex]
Step-by-step explanation:
The given polynomial is (x³+ 6x²+ 3x + 1) and we have to divide this polynomial by (x - 2) using synthetic division.
In synthetic division, we divide coefficients of the given terms of the polynomial by (x -2) = 0 ⇒ x = 2
So, 2| 1 6 3 1 ---------[ coefficients]
2 16 38
1 8 19 39
Let me explain it. In first row i have written the coefficients of the terms given in the polynomial 1.x³ + 6.x² + 3x + 1
In the first row I have written 2 in the left side before 1. This is the number by which i am going to divide the coefficients written in the first row.
Now I copied 1 at the bottom (below the line).
Then 2×1 = 2 (written in second row) added with 6 gave 8 at the bottom.
then 8×2 = 16 (written in second row) added with 3 gave 19 at the bottom.
19×2 = 38 (written in second row) added with 1 gave 39 at the bottom.
Now we will rewrite the expression
[1.(x)²+ 8.(x) + 19] + [tex]\frac{39}{(x - 2)}[/tex]
Here highlighted part give in the bracket is the quotient and 19 is the remainder.
