Help with this question!

Question

What is an example of a polynomial you could add to h(x) to generate a polynomial with a degree of 5?

h(x) = -3x^6 + 2x^4 - 3x^2

Answer 1

Hello Jacqueline G.,

A polynomial of degree 5 would have a highest exponent of x equal to 5. So you have to cancel out the -3x⁶.

What would you add to -3x⁶ to cancel it out? Also, since there is not term with x ^ 5, you will also need to add a nonzero term with x ^ 5. (It could just be x ^ 5.) See if you can find the answer. You may submit your final answer to be checked by an expert.

Answer 2

Let take polynomial g(x) = 3x⁶ + x⁵; then h(x) + g(x) = - 3x⁶ + 2x⁴ - 3x² + 3x⁶ + x⁵ = x⁵ + 2x⁴ - 3x² and we get 5th degree polynomial

Answer 3

Add any polynomial that cancels the -3x⁶ term and adds a term with x⁵ in it. Example:

g(x) = 3x⁶ + x⁵

g(x) + h(x) = (3x⁶ - 3x⁶) + x⁵ + 2x⁴ - 3x² = x⁵ + 2x⁴ - 3x²

You are left with a degree 5 polynomial.