Question

How do you divide $(2{x^3} + 3{x^2} - 8x + 3) \div (x + 3)$?

Answer 1

Hint: The given division is $(2{x^3} + 3{x^2} - 8x + 3) \div (x + 3)$. One way is to use the divisor as factors in the numerator consider the numerator.
First we add and subtract by $6{x^2}$ with the first term
We take the common term $(x + 3)$ in RHS (Right Hand Side) numerator.
Divide the final part and we get the result.

Complete step by step answer:
The given division is $(2{x^3} + 3{x^2} - 8x + 3) \div (x + 3)$
One way is to use the divisor as factors in the numerator consider the numerator.
First we add and subtract by $6{x^2}$ with the first term
$ = 2{x^3} + 6{x^2} - 6{x^2} + 3{x^2} - 8x + 3$
We take the common term$2{x^2}$in the first term and second term, hence we get
$ = 2{x^2}(x + 3) - 6{x^2} + 3{x^2} - 8x + 3$
We can rewrite the third term $3{x^2}$ into add and subtract $9x$, hence we get
$ = 2{x^2}(x + 3) - 6{x^2} - 9x + 9x - 8x + 3$
Now we take common term $ - 3x$ in the second term and third term
$ = 2{x^2}(x + 3) - 3x(x + 3) + 9x - 8x + 3$
Subtract$9x$by$8x$, hence we get
$ = 2{x^2}(x + 3) - 3x(x + 3) + x + 3$
Now we take common term$1$in the last term
$ = 2{x^2}(x + 3) - 3x(x + 3) + 1(x + 3)$
$ \Rightarrow 2{x^3} + 3{x^2} - 8x + 3 = 2{x^2}(x + 3) - 3x(x + 3) + 1(x + 3)$
Substitute in the given division, hence we get
$ \Rightarrow \dfrac{{2{x^3} + 3{x^2} - 8x + 3}}{{x + 3}} = \dfrac{{2{x^2}(x + 3) - 3x(x + 3) + 1(x + 3)}}{{(x + 3)}}$
Now, we take common term $(x + 3)$ in RHS (Right Hand Side) numerator, hence we get
$ \Rightarrow \dfrac{{2{x^3} + 3{x^2} - 8x + 3}}{{x + 3}} = \dfrac{{(x + 3)(2{x^2} - 3x + 1)}}{{(x + 3)}}$
Now divide $(x + 3)(2{x^2} - 3x + 1)$ by $(x + 3)$ , hence we get
\[ \Rightarrow \dfrac{{2{x^3} + 3{x^2} - 8x + 3}}{{x + 3}} = \dfrac{{\not{{(x + 3)}}(2{x^2} - 3x + 1)}}{{\not{{(x + 3)}}}}\]

we write the final Remaining term is written below,
$ \Rightarrow \dfrac{{2{x^3} + 3{x^2} - 8x + 3}}{{x + 3}} = 2{x^2} - 3x + 1$

Note: Division of polynomials might seem like the most challenging and intimidating of the operations to master, but so long as you can recall the basic rules about the long division of integers, it’s a surprisingly easy process. A polynomial is a longer algebraic expression made up of two or more terms which are subtracted, added or multiplied. A polynomial can contain coefficients, variables, exponents, constants and operators such addition and subtraction. It is also important to note that a polynomial can’t have fractional or negative exponents.