MathDB
Counting number of polynomials

Source: 1959 AHSME Problem 48

August 14, 2013
algebrapolynomialAMC

Problem Statement

Given the polynomial a0xn+a1xn1++an1x+ana_0x^n+a_1x^{n-1}+\cdots+a_{n-1}x+a_n, where nn is a positive integer or zero, and a0a_0 is a positive integer. The remaining aa's are integers or zero. Set h=n+a0+a1+a2++anh=n+a_0+|a_1|+|a_2|+\cdots+|a_n|. [See example 25 for the meaning of x|x|.] The number of polynomials with h=3h=3 is: <spanclass=latexbold>(A)</span> 3<spanclass=latexbold>(B)</span> 5<spanclass=latexbold>(C)</span> 6<spanclass=latexbold>(D)</span> 7<spanclass=latexbold>(E)</span> 9 <span class='latex-bold'>(A)</span>\ 3\qquad<span class='latex-bold'>(B)</span>\ 5\qquad<span class='latex-bold'>(C)</span>\ 6\qquad<span class='latex-bold'>(D)</span>\ 7\qquad<span class='latex-bold'>(E)</span>\ 9