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Name Date Factoring ax 2 + bx + c 7.6 For use with Exploration 7.6 Essential Question How can you use algebra tiles to factor the trinomial ax 2 + bx + c into the product of two binomials? 1 EXPLORATION:
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How to Fill out Factoring ax 2 bx:

01
Identify the quadratic equation in the form ax^2 + bx + c = 0. In this case, we have a quadratic equation in the form ax^2 + bx, where a is the coefficient of x^2, and b is the coefficient of x.
02
Determine the factors of the coefficient of x^2 (a) and the constant term (b). Factors are the numbers that can be multiplied together to get a specific product.
03
Determine the signs of the factors. We need to find two numbers that, when multiplied, will give us the constant term (b), but when added or subtracted, will give us the coefficient of x (b).
04
Rewrite the quadratic equation using the two factors determined in step 2. This will involve splitting the bx term into two parts, using the factors found in step 3.
05
Factor by grouping or using the ac method if necessary. This step helps in simplifying and factoring the quadratic equation further.
06
Once factored, set each factor equal to zero and solve for x. This will give us the values of x that make the equation equal to zero.

Who Needs Factoring ax 2 bx:

01
Students studying algebra and quadratic equations in mathematics classes may need to learn how to factor ax^2 + bx. It is an important skill in solving and simplifying quadratic equations.
02
Engineers and scientists who work with equations involving quadratic terms may need to factor ax^2 + bx. Factoring helps in finding the roots or solutions of these equations, which are essential in solving real-life problems.
03
Financial analysts and economists may apply factoring ax^2 + bx in certain calculations or models. Quadratic equations can be used to represent various economic or business scenarios, and factoring helps in analyzing and finding solutions for these situations.
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