Question

Factor each polynomial. $$ x^{3}+4 x^{2}+3 x+12 $$

   Factor each polynomial.
$$
x^{3}+4 x^{2}+3 x+12
$$

Intermediate Algebra

Intermediate Algebra

Elayn Martin-Gay 6th Edition

Chapter 5, Problem 68

Instant Answer

Solved by Expert James Kiss

07/18/2020

Step 1

Step 1: First, we can group the terms in the polynomial as follows: $$ (x^{3}+4 x^{2})+(3 x+12) $$ Show more…

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Factor each polynomial. $$ x^{3}+4 x^{2}+3 x+12 $$

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Key Concepts

Factoring by Grouping

Factoring by grouping is a method that involves partitioning the terms of a polynomial into groups that have a common factor. By factoring each group separately and then extracting a common binomial factor, one can simplify the polynomial into a product of two or more factors.

Rational Root Theorem

The rational root theorem is a tool used to list all possible rational roots of a polynomial with integer coefficients. It involves testing combinations of the factors of the constant term and the leading coefficient, which can then be verified and used to factor the polynomial.

Factor Theorem

The factor theorem is a fundamental concept used to determine if a binomial of the form (x - c) is a factor of a polynomial. It states that if substituting c into the polynomial yields zero, then (x - c) is a factor, which helps in breaking the polynomial into simpler factors.

Polynomial Factoring

This is the process of rewriting a polynomial as a product of simpler polynomials whose multiplication gives the original polynomial. It often involves techniques like factoring by grouping, recognizing special patterns, and utilizing the factor theorem to systematically break down the expression.

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