Answer:
x⁴ - 3x² + 5
Explanation:
Given
Index = {1,0,-3,0,5}
Required
Represent as a polynomial
First, we need to get the degree (n) of the polynomial.
Because the given indices are 5,
Then
n = 5 - 1
n = 4
The polynomial is then represented as;
ax⁴ + bx³ + cx² + dx + e
Where
{a, b, c, d, e} = {1, 0, -3, 0, 5}
i.e.
a = 1 b = 0 c = -3 d = 0 e = 5
Substitute these values of a to e in the expression above:
ax⁴ + bx³ + cx² + dx + e
1x⁴ + 0x³ - 3x² + 0x + 5
x⁴ + 0 - 3x² + 0 + 5
x⁴ - 3x² + 5