Respuesta :
Answer:
The table to the right shows ordered pairs that belong to a polynomial function. If f(x) is a cubic polynomial, which conclusion is value? f(x). -14 ... If x – 2 divides p(x) evenly, which statement must be true? ... 5. Jeremiah divided the two polynomials shown. 10x2 + 23x – 14. 2x + 1. -5 ... a) 2x3 + 4x2 – 3x.
Step-by-step explanation:
The first conclusion is correct that is the remainder of p(x) divided by (x-1) is 5 and this can be determined by using the arithmetic operations.
Given :
Polynomial -- [tex]\rm p(x) = -2x^3+3x+4[/tex]
According to the given data, P(1) = 5, which means that when 5 is subtracted from p(x) then (x-1) is one of the roots of the given polynomial equation.
Check both the options in order to determine the correct conclusion.
A) The remainder of p(x) divided by (x-1) is 5.
[tex]= \dfrac{-2x^3+3x+4-5}{x-1}[/tex]
Simplify the above expression by factorizing the numerator.
[tex]= \dfrac{-2x^3+2x^2-2x^2+2x+x-1}{x-1}[/tex]
[tex]= \dfrac{-2x^2(x-1)-2x(x-1)+(x-1)}{x-1}[/tex]
[tex]=-2x^2-2x+1[/tex]
So, yes this conclusion is correct and therefore, no need to check the second conclusion.
For more information, refer to the link given below:
https://brainly.com/question/2096984
