Complete each factoring 16 p^2-4 p q-2 q^2=2(2 p-q) () |...

Name: Problem 18, Chapter 5: Algebra for College Students
Uploaded: 2022-02-19T16:36:36-08:00
Duration: 2 min 34 s
Channel: Dheeraj
Description: Complete each factoring 16 p^2-4 p q-2 q^2=2(2 p-q) ()

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Key Concepts

Greatest Common Factor (GCF) Extraction

Before factoring a polynomial further, it is often useful to first extract the greatest common factor from all terms. This simplifies the expression and makes subsequent factoring steps more straightforward. In many cases, pulling out a common numerical or variable factor can reduce the coefficients, leading to a simpler quadratic or other polynomial to factor.

Factoring Quadratic Trinomials

Factoring quadratic trinomials involves expressing a quadratic expression, typically of the form ax² + bx + c, as a product of two binomials. This requires finding two numbers that multiply to a*c and add to b. This method can be extended to quadratics in more than one variable where the factorization strategy is similar in matching coefficients.

Product-Sum Method

The product-sum method is a technique used in factoring quadratic trinomials by identifying a pair of numbers whose product equals the product of the coefficient of the squared term and the constant term, and whose sum equals the coefficient of the middle term. This method helps in decomposing the middle term to enable factoring by grouping or direct factorization into two binomials.

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