Given f(x)=4x^2-10x-3, according to the remainder theorem, f(2) can be found by finding the remainder Of which of the fallowing division quotients?
To apply the remainder theorem, we need to divide the function f(x) by a term of the form (x - a), where a represents a constant.
In this case, we are looking for the remainder when we divide f(x) by (x - 2). Therefore, the division quotient we need is (x - 2).
To apply the remainder theorem, we need to perform synthetic division. Synthetic division is used to divide a polynomial by a linear factor. In this case, we want to divide f(x) by (x - 2) since we are finding f(2).
Let's perform synthetic division:
2 | 4 -10 -3
|_________
| 8
_________________________
4 -2 5
The remainder of this division is 5.
Therefore, f(2) can be found by finding the remainder of the division quotient when dividing f(x) by (x - 2).
To apply the remainder theorem, we need to divide the given polynomial f(x) by a linear equation of the form (x - a), where 'a' is the value we want to evaluate the function at. In this case, we want to find f(2), so we need to divide f(x) by (x - 2).
By performing the division, we can write f(x) as:
f(x) = (x - 2) q(x) + r
where q(x) is the quotient and r is the remainder.
Now, by substituting x = 2 into the equation, we can find the remainder and determine f(2):
f(2) = (2 - 2) q(2) + r
f(2) = 0 * q(2) + r
f(2) = r
So, to find f(2) using the remainder theorem, we only need to know the remainder (r) from the division of f(x) by (x - 2).