Given f(x)=4x^2-10x-3, according to the remainder theorem, f(2) can be found by finding the remainder
when f(x) is divided by (x-2).
To find the remainder, we divide the polynomial f(x) by (x-2) using synthetic division:
2 | 4 -10 -3
| 8 -4
------------------
4 -2 -7
The remainder when f(x) is divided by (x-2) is -7.
Therefore, according to the remainder theorem, f(2) can be found by taking the remainder -7.
The remainder theorem states that if you divide a polynomial f(x) by a linear expression x - a, the remainder will be equal to f(a). In other words, to find the remainder when dividing f(x) by x - a, you simply substitute a into the polynomial and compute the result.
In this case, you want to find the remainder when dividing f(x) = 4x^2 - 10x - 3 by x - 2. To do this, substitute x = 2 into the polynomial:
f(2) = 4(2)^2 - 10(2) - 3
= 4(4) - 20 - 3
= 16 - 20 - 3
= -7
Therefore, the remainder when dividing f(x) by x - 2 is -7.
To find the remainder when evaluating f(2), we can use the remainder theorem.
According to the remainder theorem, if we divide the polynomial f(x) by x - c, where c is a constant, the remainder obtained is equal to f(c).
In this case, we want to find the remainder when dividing f(x) by x - 2, so we can evaluate f(2) to find it.
Substituting x = 2 into the polynomial f(x) = 4x^2 - 10x - 3, we get:
f(2) = 4(2)^2 - 10(2) - 3
= 4(4) - 20 - 3
= 16 - 20 - 3
= -4 - 3
= -7
Therefore, by evaluating f(2), we find that the remainder is -7.