Jacqueline G.

asked • 06/01/20# Help with this 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**

## 3 Answers By Expert Tutors

Tom S. answered • 06/01/20

Highly Experienced, Patient High School, College, SAT/ACT Math Tutor

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 -3x^{6}.

What would you add to -3x^{6} 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.

Yefim S. answered • 06/01/20

Math Tutor with Experience

Let take polynomial g(x) = 3x^{6} + x^{5}; then h(x) + g(x) = **- 3**x^{6} + 2x^{4} - 3x^{2} + 3x^{6} + x^{5} = x^{5} + 2x^{4} - 3x^{2} and we get 5th degree polynomial

Arturo O. answered • 06/01/20

Experienced Physics Teacher for Physics Tutoring

Add any polynomial that cancels the -3x^{6} term and adds a term with x^{5} in it. Example:

g(x) = 3x^{6} + x^{5}

g(x) + h(x) = (3x^{6} - 3x^{6}) + x^{5} + 2x^{4} - 3x^{2} = x^{5} + 2x^{4} - 3x^{2}

You are left with a degree 5 polynomial.

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Paul M.

06/01/20