Solve each equation by factoring ⁉️NEED THESE ASAP ⁉️

Answer:

3.

a=-1

a=-2

5.

n=-6

n=-3

8.

n=-5

n=-3

Step-by-step explanation:

3. separate into probable cases

[tex]a + 2 = 0\\ a + 1 = 0[/tex]

5.

[tex] {n}^{2} + 6n - 3n - 18 = 0 \\ [/tex]

factor out n from the expression

factor out -3 from the expression

[tex]n \times (n + 6) - 3(n + 6) = 0[/tex]

factor out n+6 from the equation

[tex](n + 6) \times (n - 3) = 0[/tex]

separate into probable cases

[tex]n + 6 = 0\\ n - 3 = 0[/tex]

solve the equations

[tex]n = - 6 \\ n = 3[/tex]

8.

[tex]n ^{2} + 5n + 3n + 15 = 0[/tex]

factor out n and 3 from the expression

[tex]n \times (n + 5) + 3(n + 5) = 0[/tex]

factor out n+5

[tex](n + 5) \times (n + 3) = 0[/tex]

separate into probable cases

[tex]n + 5 = 0 \\ n + 3 = 0[/tex]

solve the equations

[tex]n = - 3 \\ n = - 3[/tex]

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You may not know this, but you are home to a colony of bacteria. You may also not know it, but the health and happiness of that colony of bacteria have a direct effect on your own health and happiness. In short, if we are what we eat, then we may need to make bacteria part of our balanced breakfast.

Microbes are single-celled organisms. They are literally everywhere. Microbes are in the air we breathe, on the surfaces of everything we touch, and inside our bodies. Microbes can be bacteria, fungi, protozoa, or viruses.

A few years ago, scientists began studying the microbial life of our stomachs. Called The American Gut project, this study aims to understand the life of the bacteria that live in our digestive system. According to an article in the New York Times by Michael Pollan, the goal is to gather information on the types and amounts of bacteria in the human gut. Scientists want to describe what a normal healthy microbe and human relationship should look like inside our digestive system. While the research is still in the very early stages, scientists have learned the following:

The strongest and healthiest microbe systems are those with a lot of variety.
The guts of Americans have much less variety than the guts of other populations.
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Studying the makeup of our individual bacteria communities will help scientists get a better idea of which bacteria help human bodies. We used to think that bacteria in our bodies were invaders. This new research suggests that bacteria are part of the protective army that keeps us healthy. In fact, our bodies have a hard time recovering from medicines like antibiotics because they disrupt the balance of helpful bacteria. It seems clear from the early evidence that living with bacteria helps us resist invasion from things that make us sick.

Scientists have also learned that microbes might help our guts do things like process vitamins and important nutrients. Some microbes may help us deal with stress, or adapt to changes. Furthermore, there may come a time—in your lifetime—when illness is treated not with antibiotics, but with extra-special microbes that help us defend our bodies from illness.









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