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Assignment Problems Notice
Please do not email me to get solutions and/or answers to these problems. I will not give them out under any circumstances nor will I respond to any requests to do so. The intent of these problems is for instructors to use them for assignments and having solutions/answers easily available defeats that purpose.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
If you are looking for some problems with solutions you can find some by clicking on the "Practice Problems" link above.
Section 1.4 : Polynomials
For problems 1 – 18 perform the indicated operation and identify the degree of the result.
- Add \(10{x^5} + 2{x^3} - 1\) to \(8{x^4} - {x^3} + 16{x^2}\)
- Add \(7{t^2} - 13t + 4\) to \( - 6{t^2} + 13t - 4\)
- Subtract \( - 12{z^2} + 9z - 3\) from \({z^3} + 2{z^2} - 15z + 7\)
- Subtract \(100{x^4} - 19{x^2} - 7x\) from \(150{x^3} + 8x - 14\)
- Subtract \({w^4} + {w^3} + {w^2} + w + 1\) from \({w^5}\)
- \(6{y^2}\left( {3 - {y^2} + 2{y^3}} \right)\)
- \({x^9}\left( {{x^2} + 7x - 4} \right)\)
- \(\left( {7x - 5} \right)\left( {4 - 10x} \right)\)
- \(\left( {4 + 9{t^2}} \right)\left( {{t^3} - 3t} \right)\)
- \(\left( {1 + 8y} \right)\left( {{y^3} - 4{y^2} + 7} \right)\)
- \(7\left( {x - 9} \right)\left( {2x + 3} \right)\)
- \({z^2}\left( {1 - {z^2}} \right)\left( {1 + {z^2}} \right)\)
- \(\left( {2 - x + 4{x^2}} \right)\left( {6x + 7} \right)\)
- \(\left( {10{w^2} - 4w + 9} \right)\left( {{w^3} + 5{w^2} + 2} \right)\)
- \(10{\left( {x + 3{x^2}} \right)^2}\)
- \(\left( {1 - 5y} \right){\left( {4 + y} \right)^2}\)
- Subtract \(\left( {3 - x} \right)\left( {3 + x} \right)\) from \({x^2} - 7x + 10\)
- Subtract \({\left( {4{x^2} - 1} \right)^2}\) from \({\left( {x + 9{x^3}} \right)^2}\)
- If we multiply a polynomial with degree n and a polynomial of degree m what is the degree of the result?
- If we add 2 polynomials of degree n and m with \(n < m\) what is the degree of the result?
- If we subtract 2 polynomials of degree n and m with \(n < m\) what is the degree of the result?
- If we add two polynomials, both of degree \(n\), is it possible for the result to not be degree \(n\)? If it is possible can you give an example of two polynomials, both of degree \(n\), whose sum is not degree \(n\)?
- If we subtract two polynomials, both of degree \(n\), is it possible for the result to not be degree \(n\)? If it is possible can you give an example of two polynomials, both of degree \(n\), whose difference is not degree \(n\)?