Question
Given f(x)=4x2−10x−3, according to the Remainder Theorem, f(2) can be found by finding the remainder of which of the following division quotients?(1 point) Responses (4x2−10x−3)÷(x+2) left parenthesis 4 x squared minus 10 x minus 3 right parenthesis divided by left parenthesis x plus 2 right parenthesis (4x2−10x−3)÷(x−2) left parenthesis 4 x squared minus 10 x minus 3 right parenthesis divided by left parenthesis x minus 2 right parenthesis (4x2−10x−3)÷2 left parenthesis 4 x squared minus 10 x minus 3 right parenthesis divided by 2 (4x2−10x−3)÷x
Answers
GPT-4o mini
According to the Remainder Theorem, if you divide a polynomial \( f(x) \) by a linear divisor of the form \( (x - c) \), the remainder of that division is equal to \( f(c) \).
In this case, you want to find \( f(2) \), which means you need to evaluate \( f(x) \) at \( x = 2 \). To use the Remainder Theorem, you should divide the polynomial \( f(x) = 4x^2 - 10x - 3 \) by \( (x - 2) \).
Thus, the correct division to find \( f(2) \) is:
\[
(4x^2 - 10x - 3) \div (x - 2)
\]
So the correct response is:
**(4x²−10x−3)÷(x−2) (4 x squared minus 10 x minus 3 divided by x minus 2)**.
In this case, you want to find \( f(2) \), which means you need to evaluate \( f(x) \) at \( x = 2 \). To use the Remainder Theorem, you should divide the polynomial \( f(x) = 4x^2 - 10x - 3 \) by \( (x - 2) \).
Thus, the correct division to find \( f(2) \) is:
\[
(4x^2 - 10x - 3) \div (x - 2)
\]
So the correct response is:
**(4x²−10x−3)÷(x−2) (4 x squared minus 10 x minus 3 divided by x minus 2)**.