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Solving by Factoring

Please explain in detail the strategy, Solving by Factoring, discussed in the lesson Quadratic in Form Polynomials. Include an example with this explanation to clearly explain the process.

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Answer:

Explanation:

Solving by factoring is a strategy for solving a polynomial equation that is in quadratic form. Quadratic form means that the equation is of the form ax^2+bx+c=0, where a,b, and c are real numbers. When factoring, the goal is to express the equation as the product of two simpler equations. To do this, we must factor the quadratic equation into two linear equations, each with a single variable.

For example, consider the equation x^2+3x-4=0. To factor this equation, we can first rewrite it as (x+4)(x-1)=0. This is the same as x+4=0 and x-1=0. We can then solve each of these linear equations to find the solutions. In this case, the solutions are x=-4 and x=1.

Therefore, the strategy of solving by factoring is to rewrite a polynomial equation in quadratic form as the product of two simpler equations, and then solve each of these equations. The solutions to the original equation can then be found by solving each of the linear equations.

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