Topics for Test 2 MATH 106

The kinds of problems in the Chapter Test, who answers I've posted. The topics there include:

• All kinds of factoring: by GCF, grouping, reverse FOIL and special products:

  x² - y² = (x + y)(x – y)

  x³ - y³ = (x - y)(x² +xy + y²)

  x³ - y³ = (x - y)(x² +xy + y²)

• Solving equations by factoring

• Physics word problem: solve for t given height h of a ball thrown from a height or in an arc.

• Long division of polynomials without remainder and with remainder

• Remainder theorem: If P(x) has a factor of x – r, then the remainder P(r) = 0 (that is, r is a root).

If the remainder P(r) is not equal to zero, then x – r is not a factor of P(x).

Other:

• Number sets N, W, Z, Q, Q', R and examples of each kind. Know which sets are subsets of others.

• Rules of exponents (i.e., monomial division), including negative exponent simplification

• Numeric values of first 10 perfect squares and first 5 perfect cubes

• Showing numeric relationship using rules of exponents:

Example: 2³² - 2³¹ = 2³¹(2 – 1) = 2³¹(1) = 2³¹

• Common mistakes (freshman mistake x² + y² = (x + y)² (it doesn't!!!!!!!!!)

• (x – y) / (y – x) = -1

• Recognize what is meant by the Fundamental Theorem of Algebra (a polynomial of degree n has a unique factorization into n factors (x – r), where r is a root, and it can be a real number, a rational number, an irrational number or an imaginary number.

• Primes: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, ....

• Twin primes: e.g. 3 and 5; 5 and 7; 11 and 13; 17 and 19; 29 and 31)

• Words of the month: mundane, volition, ambient, paucity, penultimate, edify or edification

(Use two of these in sentences.)