Respuesta :
Answer: First Option is correct.
Step-by-step explanation:
Since we have given that
[tex](4x^3+2x^2-18x+38)\div(x+3)[/tex]
We will apply the "Remainder Theorem ":
So, first we take
[tex]g(x)=x+3=0\\\\g(x)=x=-3\\\\and\\\\f(x)=4x^3+2x^2-18x+38[/tex]
So, we will put x=-3 in f(x).
[tex]f(-3)=4\times (-3)^3+2\times (-3)^2-18\times (-3)+38\\\\f(-3)=-108+18+54+38\\\\f(-3)=2[/tex]
So, Remainder of this division is 2.
Hence, First Option is correct.
The remainder of the given expression is 2 and this can be determined by using the factorization method.
Given :
Expression -- [tex]\rm \dfrac{4x^3+2x^2-18x+38}{x+3}[/tex]
The factorization method can be used in order to determine the remainder of the given expression.
The expression given is:
[tex]\rm =\dfrac{4x^3+2x^2-18x+38}{x+3}[/tex]
Try to factorize the numerator in the above expression.
[tex]\rm =\dfrac{4x^3+12x^2-10x^2-30x+12x+36+2}{x+3}[/tex]
[tex]\rm = \dfrac{4x^2(x+3)-10x(x+3)+12(x+3)+2}{(x+3)}[/tex]
Simplify the above expression.
[tex]\rm = (4x^2-10x+12) + \dfrac{2}{(x+3)}[/tex]
So, the remainder of the given expression is 2. Therefore, the correct option is A).
For more information, refer to the link given below:
https://brainly.com/question/6810544
