Question

1. y=5x^3+0x^2+x+7 & y=5x^4+0x^2+1
2. Choose one integer from the following set: -5 ≤ x ≤ 5. State the integer you chose.
3. When using long division, what binomial would you divide by to determine if your chosen integer from part b is a zero for your polynomial?
4. Do the long division you just described in part c.
5. Write the answer to the long division problem in the form   .
6. Is your integer from part b a zero of your polynomial? How you can tell from the long division work.

Answer 1

$(1)\\ y_1 =5x^3+0x^2+x+7\hspace{0.1cm} \& \hspace{0.1cm} y_2=5x^4+0x^2+1\\ (2)\\ \textsf{I choose}\hspace{0.1cm}\textit{ x = 3}\\ (3)\\ \textsf{If} \hspace{0.1cm}\textit{3}\hspace{0.1cm} \textsf{is a zero of}\hspace{0.1cm} y_2,\\ \textsf{then}\hspace{0.1cm} \textit{x - 3}\hspace{0.1cm} \textsf{would be a factor of}\hspace{0.1cm} y_2,\\\textsf{which implies that the}\\\textsf{ binomial to be divided}\\\textsf{by}\hspace{0.1cm}y_2 \hspace{0.1cm}\textsf{to give a remainder}\\\textsf{is}\hspace{0.1cm}\textit{ x - 3.}\\ (5) \textsf{The remainder is}\hspace{0.1cm} \textit{145}\\ (6) \textsf{No, my integer from part b}\\\textsf{is not a zero of my polynomial,}\\ \textsf{because the remainder after}\\\textsf{ the long division is not equal to}\hspace{0.1cm} \textit{0}.$