Difference between revisions of "1988 AHSME Problems/Problem 15"

Revision as of 01:59, 23 October 2014

If $a$ and $b$ are integers such that $x^2 - x - 1$ is a factor of $ax^3 + bx^2 + 1$ , then $b$ is

$\textbf{(A)}\ -2\qquad \textbf{(B)}\ -1\qquad \textbf{(C)}\ 0\qquad \textbf{(D)}\ 1\qquad \textbf{(E)}\ 2$

1988 AHSME (Problems • Answer Key • Resources)
Preceded by Problem 14	Followed by Problem 16
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30
All AHSME Problems and Solutions

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-Suppose that <math>a</math> and <math>b</math> are integers such that <math>x^2-x-1</math> is a factor of <math>ax^3+bx^2+1</math>. What is <math>b</math>?
+==Problem==
+If <math>a</math> and <math>b</math> are integers such that <math>x^2 - x - 1</math> is a factor of <math>ax^3 + bx^2 + 1</math>, then <math>b</math> is
+<math>\textbf{(A)}\ -2\qquad
+\textbf{(B)}\ -1\qquad
+\textbf{(C)}\ 0\qquad
+\textbf{(D)}\ 1\qquad
+\textbf{(E)}\ 2</math>
+==Solution==
+== See also ==
+{{AHSME box|year=1988|num-b=14|num-a=16}}
+[[Category: Intermediate Algebra Problems]]
 {{MAA Notice}}