A polynomial is represented as: [tex]ax^n + bx^{n - 1} + ...... + cx + d[/tex].
- The polynomial divisor is [tex]x + 3[/tex].
- The dividend is [tex]2x^3 + 11x^2 + 18x + 9[/tex].
- The quotient is [tex]2x^2 + 5x + 3[/tex].
See attachment for the illustration of the synthetic division of a polynomial.
Using the attachment as a guide;
The divisor (D) is as follows:
[tex]D - 3 = x[/tex]
Add 3 to both sides
[tex]D = x + 3[/tex]
The dividend (P) is as follows:
[tex]P =9 + 18x + 11x^2 + 2x^3[/tex]
Rewrite as:
[tex]P =2x^3 + 11x^2 +18x + 9[/tex]
The quotient (Q) is as follows:
[tex]Q = 3 + 5x + 2x^2[/tex]
Rewrite as:
[tex]Q= 2x^2 +5x + 3[/tex]
Hence:
The divisor of the polynomial is [tex]x + 3[/tex], while the dividend and the quotient are [tex]2x^3 + 11x^2 + 18x + 9[/tex] and [tex]2x^2 + 5x + 3[/tex], respectively.
Read more about synthetic divisions of polynomials at:
https://brainly.com/question/2568440
