Answer to Question #135729 in Calculus for Everlyn

Question

y=5x^3+0x^2+x+7
Choose one integer from the following set: -5 ≤ x ≤ 5. State the integer you chose.
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?
Do the long division you just described in part c.
Write the answer to the long division problem in the form .
Is your integer from part b a zero of your polynomial? How you can tell from the long division work.

Answer 1

$(a)\\ y = 5x^3 + 0x^2 + x + 7\\ (b)\\ \textsf{I choose}\hspace{0.1cm}\textit{ x = 3}\\ (c)\\ \textsf{If} \hspace{0.1cm}\textit{3}\hspace{0.1cm} \textsf{is a zero of}\hspace{0.1cm} y,\\ \textsf{then}\hspace{0.1cm} \textit{x - 3}\hspace{0.1cm} \textsf{would be a factor of}\hspace{0.1cm} y,\\\textsf{which implies that the}\\\textsf{binomial to divide}\\\hspace{0.1cm}y \hspace{0.1cm}\textsf{intended to give a remainder}\\\textsf{of zero is}\hspace{0.1cm}\textit{ x - 3.}\\ (e) \textsf{Answer: the remainder is}\hspace{0.1cm} \textit{145}\\ (f) \textsf{No, the integer from part }\hspace{0.1cm} b\\\textsf{is not a zero of the polynomial,}\\ \textsf{because the remainder after}\\\textsf{the long division is not equal to}\hspace{0.1cm} \textit{0}.$