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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 factored form of the given trinomial \(x^{2}-14 x+45\) is \((x-9)(x-5)\)

Step by step solution

01

Identify a, b, and c

In the trinomial \(x^{2}-14 x+45\), the coefficients of \(x^{2}\), \(x\), and the constant term are a=1, b=-14, and c=45, respectively.
02

Find two numbers with desired properties

We need to find two numbers that add up to -14 and their product is \(1*45 = 45\). Those numbers are -9 and -5, since \(-9 + -5 = -14\) and \(-9 * -5 = 45\).
03

Rewrite the trinomial as two binomial factors

Use the numbers found to rewrite the trinomial. The factored form of the given trinomial \(x^{2}-14 x+45\) will be \((x-9)(x-5)\).

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