Question

True or False $3 x^{3}-2 x^{2}-6 x+4=(3 x-2)\left(x^{2}+2\right)$

   True or False $3 x^{3}-2 x^{2}-6 x+4=(3 x-2)\left(x^{2}+2\right)$

College Algebra

College Algebra

Michael Sullivan 10th Edition

Chapter 0, Problem 8

Instant Answer

Solved by Expert Patrick Burns

05/08/2020

Step 1

This means we multiply $(3x-2)$ with each term inside the brackets $(x^{2}+2)$. Show more…

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True or False $3 x^{3}-2 x^{2}-6 x+4=(3 x-2)\left(x^{2}+2\right)$

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Key Concepts

Distributive Property

The distributive property is a fundamental principle in algebra that states a(b + c) = ab + ac. This property is used extensively in polynomial multiplication, allowing one to expand expressions and simplify them by distributing a multiplier across terms within parentheses.

Comparison of Polynomial Coefficients

When determining whether two polynomial expressions are equal, it is necessary to compare the coefficients of corresponding powers of the variable. For two polynomials to be exactly equal, every matching term must have the same coefficient, ensuring that the expressions are identical for all values of the variable.

Polynomial Multiplication

Polynomial multiplication involves taking each term of one polynomial and multiplying it by every term of the other polynomial. This process is essential for expanding products of polynomials and verifying whether a proposed factorization is correct.

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