Answer:
x² + ax + 3 is 2
Explanation:
To find the value of "a" in the polynomial f(x) = x² + ax + 3, we have the condition that the remainder when divided by (x-1) is three times the remainder when divided by (x+1).
To solve this problem, we can use the Remainder Theorem. According to the Remainder Theorem, if we divide a polynomial f(x) by (x - c), the remainder will be f(c).
So, let's divide the polynomial f(x) by (x - 1) and (x + 1) to find the remainder and set up an equation:
Dividing f(x) by (x - 1):
Remainder = f(1)
= (1)² + a(1) + 3
= 1 + a + 3
= a + 4
Dividing f(x) by (x + 1):
Remainder = f(-1)
= (-1)² + a(-1) + 3
= 1 - a + 3
= 4 - a
According to the given condition, the remainder when divided by (x - 1) is three times the remainder when divided by (x + 1):
a + 4 = 3(4 - a)
Now, let's solve this equation for "a":
a + 4 = 12 - 3a
4a = 8
a = 2
Therefore, the value of "a" in the polynomial f(x) = x² + ax + 3 is 2.