Question

In Exercises $1-22,$ solve by factoring. $x^{2}-5 x+6=0$

   In Exercises $1-22,$ solve by factoring.
$x^{2}-5 x+6=0$

Algebra and Trigonometry

Algebra and Trigonometry

Cynthia Y. Young 4th Edition

Chapter 1, Problem 1

Instant Answer

Solved by Expert Trinity Steen

06/14/2021

Step 1

We are looking for two numbers that multiply to 6 (the constant term) and add to -5 (the coefficient of the x term). The numbers -2 and -3 satisfy these conditions. So, we can write the equation as $(x-2)(x-3)=0$. Show more…

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In Exercises $1-22,$ solve by factoring. $x^{2}-5 x+6=0$

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Key Concepts

Quadratic Equations

A quadratic equation is an equation of the form ax² + bx + c = 0, where a, b, and c are constants with a ? 0. These equations have two solutions, which can be real or complex numbers, and can be solved using various methods including factoring, completing the square, and the quadratic formula.

Factoring Polynomials

Factoring is the process of rewriting a polynomial as a product of simpler polynomials or expressions. In the context of quadratic equations, factoring involves finding two binomials whose product equals the original quadratic expression. This technique simplifies finding the roots of the equation by reducing it to simpler components.

Zero Product Property

The Zero Product Property states that if a product of two factors equals zero, then at least one of the factors must be zero. This principle is used to solve factored equations: after expressing a quadratic as a product of factors, setting each factor equal to zero yields the potential solutions of the equation.

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