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Chapter 0: Problem 19

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

Short Answer

Expert verified
The factored form of \(x^{2}-2x-15\) is \((x+3)(x-5)\).

Step by step solution

01

Identify 'a', 'b' and 'c'

From our given trinomial \(x^{2}-2x-15\), we identify a = 1, b = -2, and c = -15. These are the coefficients and constant of the trinomial.
02

Look for two numbers that satisfy the conditions

Now, we try to look for two numbers that add up to -2 (b) and multiply to -15 (c). With trial and error, we conclude that these two numbers are -5 and 3 because \(-5 + 3 = -2\) and \(-5 * 3 = -15\)
03

Rewrite the Trinomial

Now that we have these two numbers, we use them to rewrite our original trinomial. Instead of \(x^{2}-2x-15\), we can write it as \((x+3)(x-5)\). This is the factored version of our trinomial.

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Most popular questions from this chapter

Perform the indicated operations. Simplify the result, if possible. $$\frac{a b}{a^{2}+a b+b^{2}}+\left(\frac{a c-a d-b c+b d}{a c-a d+b c-b d} \div \frac{a^{3}-b^{3}}{a^{3}+b^{3}}\right)$$

Explain how to multiply rational expressions.

Will help you prepare for the material covered in the first section of the next chapter. If \(y=|x+1|,\) find the value of \(y\) that corresponds to values of \(x\) for each integer starting with -4 and ending with 2

In Exercises \(133-136\), determine whether each statement is true or false. If the statement is false, make the necessary change(s) to produce a true statement. $$\frac{\sqrt{20}}{8}=\frac{\sqrt{10}}{4}$$

Determine whether each statement makes sense or does not make sense, and explain your reasoning. I subtracted \(\frac{3 x-5}{x-1}\) from \(\frac{x-3}{x-1}\) and obtained a constant.
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