If f, of, x, equals, 2, x, to the power 5 , plus, 5, x, minus, 1f(x)=2x
5
+5x−1, then what is the remainder when f, of, xf(x) is divided by x, plus, 3x+3?
Solve the problem just like the example below
⬇️
If
f, of, x, equals, 5, x, squared, minus, 4
f(x)=5x
2
−4, then what is the remainder when
f, of, x
f(x) is divided by
x, minus, 2
x−2?
Use the remainder theorem:
Use the remainder theorem:
The remainder of , f, of, x, divided by, left parenthesis, x, minus, 2, right parenthesis, equals , f, of, 2
The remainder of f(x)÷(x−2) equals f(2)
f, of, 2, equals, 5, left parenthesis, 2, right parenthesis, squared, minus, 4
f(2)=5(2)
2
−4
16
16
The slow way:
The slow way:
x, minus, 2
x−2
5, x, squared
5x
2
minus, 4
−4
2
2
5
5
0
0
minus, 4
−4
down arrow
↓
10
10
20
20
5
5
10
10
16
16
1 answer
Let's solve the problem step-by-step, using the remainder theorem and following the format of your example.
We are given the function:
\[ f(x) = 2x^5 + 5x - 1 \]
We need to find the remainder when \( f(x) \) is divided by \( x + 3 \).
Use the Remainder Theorem:
The remainder of \( f(x) \) when divided by \( (x + 3) \) is equal to \( f(-3) \).
Calculate \( f(-3) \):
Substituting \( -3 \) into the function:
\[
f(-3) = 2(-3)^5 + 5(-3) - 1
\]
