college algebra p5

P.5 is about what to do with fractions with polynomials in them

DomainSimplify (factor and cancel)

Multiply and Divide

“Find the Domain”all possible values for x

Domain of A

polynomial

Domain of

a graphwill learn this one in unit three when we do all the graphing stuff

is always “All Real Numbers”set bottom

not equal to zero and solve

set stuff greater than or equal to zero and solve

Domain of a polynomial

• The “domain” answers the question “What can x be?” not in a solve-this-equation kind of way, but more often when it is not possible to solve. The domain is a description of all the real values that are allowed to be used for x.

• In polynomials, x can be any real number. In 2x3 + 3x + 4, x could be a million zillion, and it’s mathematically legal. So for any polynomial, the DOMAIN is “All real numbers.”

What in the world would be NOT allowed?

• Mathematical Illegalities for us:– Dividing by Zero.– Taking an Even Root of a Negative.These are the only two we know about this

semester.

or

People ask…

• In that last one, people ask “but what do you do with the x + 3?” NOTHING. We are just playing police and looking for the illegalities. The top could have been anything. The important thing is that we are not letting the DENOMINATOR be zero.

Find the domain of 2x

The stuff underneath an even-indexed radical canNOT be negative.

So, x – 2 cannot be negative. The question was “What can x be?”

Algebraically, I will set x – 2 ≥ 0 and solve for x.

DOMAIN:

Which one of these is correct?

When cancelling vertically, you can only cancel factors not terms.

In other words, when cancelling vertically, there must be a times sign in the numerator or denominator, not a plus.

Simplify (factor & cancel)

• 1. Factor top completely.• 2. Factor bottom completely.• 3. Cancel out any factors that appear in the top and

bottom.

4

1026

Simplify 63

1242

x

xx

Multiply and Divide

• 1. Factor everything.• 2.Don’t forget to “keep it, change it, flip it”

when you are dividing.• 3. Cancel common factors vertically.• 4. Include domain restrictions. “x ≠..”

xx

xxx

xx

xx

64

23

54

622

23

2

2

Don’t forget domain restrictions for those denominators that got cancelled.

7

213

49

49142

2

x

x

x

xx