If f, left bracket, x, right bracket, equals, 5, x, to the power 5 , plus, 3, x, cubed, plus, 2f(x)=5x
5
+3x
3
+2, then what is the remainder when f, left bracket, x, right bracketf(x) is divided by x, minus, 2x−2?
To find the remainder when f(x)f(x) is divided by x−2x−2, we can use the remainder theorem. According to the remainder theorem, if f(a) is divided by (x−a), the remainder will be f(a).
In this case, we can plug in x=2x=2 into f(x)f(x) to find the remainder.
f(2) = 5(2)^5 + 3(2)^3 + 2f(2) = 5(32) + 3(8) + 2f(2)
Since we don't know the value of f(2), we cannot determine the exact value of the remainder.
Therefore, the remainder when f(x)f(x) is divided by x−2x−2 is 5(32) + 3(8) + 2f(2).
To find the remainder when f(x) is divided by x - 2, we can use the Remainder Theorem. The Remainder Theorem states that if you divide a polynomial f(x) by x - a, the remainder is equal to f(a).
In this case, we need to find the remainder when f(x) is divided by x - 2. So, we need to substitute x = 2 into f(x) and find the value.
Let's calculate f(2):
f(2) = 5(2)^5 + 3(2)^3 + 2(5)(2) + 3(2) + 2
= 5(32) + 3(8) + 10(2) + 6 + 2
= 160 + 24 + 20 + 6 + 2
= 212.
Therefore, the remainder when f(x) is divided by x - 2 is 212.
To find the remainder when f(x)f(x) is divided by x - 2x - 2, we can use the Remainder Theorem.
The Remainder Theorem states that if a polynomial f(x)f(x) is divided by x - ax - a, then the remainder is equal to f(a)f(a).
In this case, f(a)f(a) represents the polynomial f(x)f(x) evaluated at x = 2x = 2.
Let's substitute x = 2x = 2 into the given polynomial f(x)f(x) and calculate the remainder.
f(2) = 5(2)^5 + 3(2)^3 + 2(5) + 3(2) + 2
= 5(32) + 3(8) + 10 + 6 + 2
= 160 + 24 + 10 + 6 + 2
= 202
Therefore, the remainder when f(x)f(x) is divided by x - 2x - 2 is 202.