Question

Use synthetic division to solve (4 x cubed minus 3 x squared 5 x 6) divided by (x 6). what is the quotient?

Answer 1

Polynomials are expressions. The solution of the division can be written as $4x^2-27x+167-\dfrac{996}{x+6}$.

What is a polynomial?

Polynomial is an expression that consists of indeterminates(variable) and coefficient, it involves mathematical operations such as addition, subtraction, multiplication, etc, and non-negative integer exponentials.

The division of the polynomial  (4x³-3x²+5x+6) when divided by (x+6), can be done in the following manner,

$\dfrac{4x^3-3x^2+5x+6}{x+6}$

$=4x^2+\dfrac{-27x^2+5x+6}{x+6}$

$=4x^2-27x+\dfrac{167x+6}{x+6}$

$=4x^2-27x+167+\dfrac{-996}{x+6}\\\\\\=4x^2-27x+167-\dfrac{996}{x+6}$

Hence, the solution of the division can be written as $4x^2-27x+167-\dfrac{996}{x+6}$.

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