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Chapter 0: Problem 22

Factor each trinomial, or state that the trinomial is prime. $$x^{2}-14 x+45$$

Short Answer

Expert verified
The trinomial \(x^{2}-14x+45\) factorises to \((x+9)(x+5)\).

Step by step solution

01

Recognizing the Structure

The given trinomial has the general structure of a quadratic equation, written in the form of \(ax^{2}+bx+c\) where \(a = 1, b = -14\), and \(c = 45\). We aim to factorise this equation into two binomials of the form \((x-p)(x-q)\), where \(p\) and \(q\) are the roots of the equation.
02

Finding Values

We need to find two numbers that multiply to \(a*c = 1*45 = 45\) and add up to \(b = -14\). The numbers that satisfy these conditions are \(-9\) and \(-5\) since \(-9*-5 = 45\) and \(-9 - 5 = -14\).
03

Writing Factorized Form

We substitute \(p\) and \(q\) with \(-9\) and \(-5\) respectively. Thus, our factorised form of the equation becomes: \((x+9)(x+5)\)

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Most popular questions from this chapter

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