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Chapter 0: Problem 139

Factor completely. $$-x^{2}-4 x+5$$

Short Answer

Expert verified
The factorized form of the given quadratic expression \(-x^2 - 4x + 5\) is \((x + 5)(-x + 1)\).

Step by step solution

01

Identify the terms of the expression

The given quadratic equation is \(-x^2 - 4x + 5\). Here, \(a = -1\), \(b = -4\), and \(c = 5\).
02

Search for the pair of numbers

We need to find two numbers which sum up to -4 (the coefficient of 'x') and whose product is 5 (the constant term). After some trials, we find that these two numbers are -5 and 1. Because \(-5 + 1 = -4\) and \(-5 * 1 = 5\).
03

Rewrite and factor

Rewrite the original quadratic expression by replacing the middle term (-4x) with -5x + x: That gives us \(-x^2 - 5x + x + 5\). Now, we can group the terms and factor by grouping: \(-x^2 - 5x + x + 5 = -x(x + 5) + 1(x + 5) = (x + 5)(-x + 1)\).

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Most popular questions from this chapter

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

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Describe two ways to simplify \(\frac{\frac{3}{x}+\frac{2}{x^{2}}}{\frac{1}{x^{2}}+\frac{2}{x}}\).

Perform the indicated operations. Simplify the result, if possible. $$\left(\frac{2 x+3}{x+1} \cdot \frac{x^{2}+4 x-5}{2 x^{2}+x-3}\right)-\frac{2}{x+2}$$
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