Find a Polynomial Given two Remainders and a Factor - Grade 12

Given two remainders and their corresponding divisors as well as a factor of a polynomial, the solution to find the polynomial is presented. The polynomial is first written as P(x) = x^3 + b x^2 + cx + d since it is a polynomial of degree 3 and its leading coefficient is equal to 1. The coefficients b, c, and d are found by writing 2 equations using the remainder theorem which states that the remainder of the division P(x) / (x - k) is equal to P(k). Also since (x - 1) is a factor, P(1) = 0. We, therefore, end up with a system of three linear equations in three variables b, c, and d which is solved, and hence the polynomial is completely determined once a, b and c are found. More from Grade 12 Math Practice at https://www.analyzemath.com/high_school_math/grade_12/grade-12-practice.html More math videos at https://www.analyzemath.com/math-videos.html. More math problems with solutions at https://www.analyzemath.com