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Chapter 6: Problem 89

Explain how to factor \(x^{2}-5 x+6\).

Short Answer

Expert verified
The factored form of \(x^{2} - 5x + 6\) is \((x - 2)(x - 3)\).

Step by step solution

01

Identify the coefficients and constant

In the equation \(x^{2} - 5x + 6\), -5 is the coefficient of the 'x' term and 6 is the constant.
02

Find the two numbers

Find two numbers that add up to -5 and multiply to 6. Upon inspection, we find that -2 and -3 satisfy these conditions, since (-2) + (-3) = -5 and (-2)*(-3) = 6.
03

Rewrite the equation

Rewrite the equation \(x^{2} - 5x + 6\) as \(x^{2} - 2x - 3x + 6\).
04

Factor by grouping

Factor by grouping, which involves taking out the common factors from the first two terms and the last two terms. This will yield: \(x(x - 2) - 3(x - 2)\).
05

Pull out the common binomial term

Pull out the common binomial term \((x - 2)\) from each term to get the answer: \((x - 2)(x - 3)\). This is the factored form of the given quadratic equation.

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Most popular questions from this chapter

Solve the quadratic equations by factoring. \(x^{2}-2 x-15=0\)

Solve the equations using the quadratic formula. \(x^{2}+4 x=6\)

In Exercises 98-99, find all positive integers b so that the trinomial can be factored. \(x^{2}+b x+15\)

Solve the quadratic equations by factoring. \(x^{2}-14 x=-49\)

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I simplified \(\frac{3+2 \sqrt{3}}{2}\) to \(3+\sqrt{3}\) because 2 is a factor of \(2 \sqrt{3}\).
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