step 1 Given expression is 2x to the 4th power minus 26 x cubed minus 96 x squared. To find out the fac

Question

$$ 2 x^{4}-26 x^{3}-96 x^{2} $$

Name: Problem 37, Chapter 5: Introductory and Intermediate Algebra for College Students
Uploaded: 2020-09-20T08:09:09-08:00
Duration: 3 min 47 s
Channel: Pammi Eswari
Description: 2 x^4-26 x^3-96 x^2

   
$$
2 x^{4}-26 x^{3}-96 x^{2}
$$

Introductory and Intermediate Algebra for College Students

Robert Blitzer 6th Edition

Chapter 5, Problem 37

Instant Answer

Solved by Expert Pammi Eswari

09/20/2020

Step 1

The GCF of $2x^{4}$, $-26x^{3}$, and $-96x^{2}$ is $2x^{2}$. Show more…

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$$ 2 x^{4}-26 x^{3}-96 x^{2} $$

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Key Concepts

Polynomial Factorization

Polynomial factorization involves rewriting a polynomial as a product of simpler polynomials or factors. This process simplifies the expression and can reveal properties such as roots or zeros of the polynomial, which is useful in solving equations or analyzing graph behavior.

Greatest Common Factor (GCF)

The greatest common factor is the largest expression that divides each term of a polynomial evenly. Extracting the GCF simplifies the polynomial and often makes subsequent factorization steps easier by reducing the degree of each term in the remaining expression.

Factoring Quadratic Expressions

After extracting common factors from a polynomial, one may be left with a quadratic expression that can be factored further. This process involves finding two numbers that multiply to the constant term and add to the coefficient of the linear term, thereby rewriting the quadratic as a product of two binomials.

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