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Chapter 0: Problem 21

Factor each trinomial, or state that the trinomial is prime. $$x^{2}-8 x+15$$

Short Answer

Expert verified
The trinomial \(x^{2}-8 x+15\) can be factored as \((x - 5)(x-3)\).

Step by step solution

01

Understand the nature of trinomial

The trinomial follows a quadratic form \(ax^{2} + bx + c\). Here \(a = 1\), \(b = -8\), and \(c = 15\). We are required to find two numbers 'm' and 'n' such that, they add up to -8 (the coefficient of 'x') and when multiplied, give 15 (constant term).
02

Find 'm' and 'n'

Finding two numbers that satisfy the above conditions might involve some trial and error. In this case, the numbers -5 and -3 are the ones we're looking for because (-5) + (-3) = -8 and -5 * -3 = 15. Hence 'm' and 'n' are -5 and -3.
03

Factor the trinomial

The original trinomial \(x^{2}-8 x+15\) can be factored as \((x - 5)(x - 3)\). It's always a good idea to check the factoring by multiplying the two binomials back together and making sure that you get the original trinomial.

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Most popular questions from this chapter

Exercises \(142-144\) will help you prepare for the material covered in the next section. Simplify and express the answer in descending powers of \(x\) : $$ 2 x\left(x^{2}+4 x+5\right)+3\left(x^{2}+4 x+5\right) $$

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. An elevator at a construction site has a maximum capacity of 3000 pounds. If the elevator operator weighs 245 pounds and each cement bag weighs 95 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

Use the strategy for solving word problems, modeling the verbal conditions of the problem with a linear inequality. An elevator at a construction site has a maximum capacity of 2800 pounds. If the elevator operator weighs 265 pounds and each cement bag weighs 65 pounds, how many bags of cement can be safely lifted on the elevator in one trip?

When graphing the solutions of an inequality, what does a parenthesis signify? What does a square bracket signify?

Determine whether each statement makes sense or does not make sense, and explain your reasoning. When checking a radical equation's proposed solution, I can substitute into the original equation or any equation that is part of the solution process.
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