Question

Factor by grouping. $$9 x^{2}+12 x+4$$

   Factor by grouping.
$$9 x^{2}+12 x+4$$

Prealgebra and Introductory Algebra

Prealgebra and Introductory Algebra

Richard N. Aufmann,… 3rd Edition

Chapter 10, Problem 93

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Solved by Expert Nez Nikoo

06/26/2020

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The numbers 6 and 6 satisfy these conditions. Show more…

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Factor by grouping. $$9 x^{2}+12 x+4$$

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Key Concepts

Perfect Square Trinomials

A perfect square trinomial is a quadratic expression that can be expressed as the square of a binomial. Recognizing this pattern, where the first and last terms are perfect squares and the middle term is twice the product of their square roots, allows for a quick and efficient factorization.

Factoring Quadratic Expressions

This concept involves rewriting a quadratic polynomial, typically in the form ax² + bx + c, as a product of two binomial expressions. Successfully factoring quadratics is fundamental in solving quadratic equations, simplifying algebraic expressions, and analyzing functions.

Factor by Grouping

Factor by grouping is a technique used to factor polynomials when they have four or more terms, although it can also be adapted to work with quadratics. The method involves dividing the polynomial into groups that have a common factor and then factoring out these common factors to reveal a common binomial factor.

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