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Chapter 0: Problem 18

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

Short Answer

Expert verified
The factors of \(x^{2}+8 x+15\) are (x + 3)(x + 5).

Step by step solution

01

Identify b and c in the trinomial

The trinomial here is in the form ax虏 + bx + c; in this case, a = 1, b = 8, and c = 15.
02

Determine factors of +15

Find pairs of numbers that multiply to give +15. These are: (+1, +15), and (+3, +5).
03

Select the correct pair of factors

From the pairs in step 2, choose the one that adds up to +8. This is the pair (+3, +5).
04

Write the factors of the trinomial

Substitute the numbers from the chosen pair into this format: (x + m)(x + n), where m and n are the numbers from the pair. Hence, the trinomial factored form will be (x + 3)(x + 5).

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Most popular questions from this chapter

Describe how to solve an absolute value inequality involving the symbol \(>.\) Give an example.

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

Explain how to divide rational expressions.

Exercises \(142-144\) will help you prepare for the material covered in the next section. Use the distributive property to multiply: $$ 2 x^{4}\left(8 x^{4}+3 x\right) $$

Determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. The equation \(a x^{2}+c=0, a \neq 0,\) cannot be solved by the quadratic formula.
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