Question

If f(x) = 2x⁴- 3x² - 2x+5 and g(x)= x³ - 2x - 3, find the sum of polynomials f(x) and g(x) and hence state the order of the sum.

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Answer 1

2x⁴ + x³ - 3x² - 4x + 2

4

Explanation:

Given functions:

f(x) = 2x⁴ - 3x² - 2x + 5

g(x) = x³ - 2x - 3

Unknown:

Sum of the polynomials = ?

Order of the sum = ?

Solution:

The sum of the polynomial is expressed as;

f(x) + g(x) = 2x⁴ - 3x² - 2x + 5 + x³ - 2x - 3

= 2x⁴ + x³ - 3x² - 2x - 2x + 5 -3

= 2x⁴ + x³ - 3x² - 4x + 2

The order of the sum is the highest power which 4.

This polynomial is of the 4th order.