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Chapter 6: Problem 86

Give two helpful suggestions for factoring \(x^{2}-5 x+6\)

Short Answer

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

Step by step solution

01

Identify 'b' and 'c' from the given polynomial

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

Identify two numbers

Now, we need to identify two numbers such that they add up to 'b' (-5 in this case) and multiply to 'c' (+6 in this case). After careful consideration, we will see that -2 and -3 will satisfy these conditions as (-2) + (-3) = -5 and (-2) * (-3) = 6.
03

Apply Identified Numbers to Factorize

Substitute -2 and -3, which were identified in step 2, into the standard format (\(x-p\)(\(x-q\)). This will give us the factored form of the given polynomial as \((x+2)(x+3)\).

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Most popular questions from this chapter

Exercises 150鈥�152 will help you prepare for the material covered in the next section. Factor: \((x-2)(x+3)-6\)

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$y^{9}-y^{5}$$

Now let's move on to factorizations that may require two or more techniques. Factor completely, or state that the polynomial is prime. Check factorizations using multiplication or a graphing utility. $$100 y^{2}+49$$

Describe a strategy that can be used to factor polynomials.

Factor completely. $$x^{2}+14 x+49-16 a^{2}$$
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