Track / Stage 4 / 42 of 340 #302 of 2000

Problem 302

AMC 12 late, AIME early

Algebra Difficulty 4.6 Find the answer

G7.4 If $x+k$ is a factor of $3 x^{2}+14 x+a$ , find $k$ . ( $k$ is an integer.)

Your answer

Official solution

$\begin{array}{l}3(-k)^{2}+14(-k)+8=0 \\ \Rightarrow 3 k^{2}-14 k+8=0 \\ (3 k-2)(k-4)=0 \\ \left.\Rightarrow k=4 \quad \text { (reject } \frac{2}{3}\right)\end{array}$

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.