2728RationalExpressions

Question 1

How do you add polynomials?

Answer 1

Add like terms.

Question 2

What will the degree of the sum of 2 polynomial equations be?

Answer 2

The highest degree in the larger of the 2 polynomials.

Question 3

How do you subtract one polynomial equation from another?

What should you look out for?

Answer 3

Subtract like terms.

Watch for - -

Question 4

How do you multiply 2 polynomials?

What will the degree be?

Answer 4

Add the exponents.

Higher than the highest of the 2 equations.

Question 5

What is

3x²(6x³ - 4x² + 7)?

Answer 5

18x⁵ - 12x⁴ + 21x²

Question 6

What method do you use to divide poynomials?

Answer 6

Long division.

Question 7

What is

^{(x² + 10x + 21)}/_{(x + 3)}

Answer 7

(x + 7)

Question 8

What is the division of one polynomial by another called?

Answer 8

A Rational Expression

Question 9

Where does that term come from?

Answer 9

Ratio

Question 10

How do you simplify Rational Expressions before you solve them?

Answer 10

Factor them out and look for common factors.

Question 11

Simplify
(4x + 12)/(9x + 27)

Answer 11

4(x + 3)/9(x + 3)
= 4/9

Question 12

How do you add or subtract rational expressions?

Answer 12

Make common denominators

Question 13

⁴/_25x + ²³/₁₀₀

Answer 13

Common denominator 100x:
16/100x + 23x/100x

= (23x + 16)/100x

Question 14

Solve:
x/(2x + 1) + 5/(x - 1)

Answer 14

x(x - 1) + 5(2x + 1)/(2x + 1)(x - 1)
(x² + 9x + 5)/(2x² - x - 1)

Question 15

Solve:
x/(x² - 9) - x/(x² + 6x + 9)

Answer 15

x/(x - 3)(x + 3) - x/(x + 3)(x + 3)
LCD = (x + 3)(x + 3)²
(x - 3) - x(x + 3)/(x - 3)(x + 3)²

= 6x/(x - 3)(x + 3)²