Vocabulary & Basics
$100 This term describes the highest exponent in a polynomial.
What is the degree?
$100 The result of (3x + 2) + (5x − 7).
What is 8x − 5?
$100 The completely factored form of x² − 9.
What is (x + 3)(x − 3)?
$100 The x-values where a polynomial's graph crosses the x-axis.
What are zeros (or roots)?
$100 What two elements determine the end behavior of a graphed polynomial function?
What is the leading coefficient and degree?
$200 A polynomial with exactly two terms, like 3x + 5.
What is a binomial?
$200 When you multiply (x + 3)(x − 3), you get this special product.
What is x² − 9 (difference of squares)?
$200 Factor x² + 7x + 12.
What is (x + 3)(x + 4)?
$200 The zeros of (x − 2)(x + 5).
What are x = 2 and x = −5?
$200 These two concepts are included in the "extrema."
What is relative (local) max/min?
$300 The numerical factor of a term, such as the 7 in 7x².
What is a coefficient?
$300 Expand (x + 4)².
What is x² + 8x + 16?
$300 Factor 2x² − 8x.
What is 2x(x − 4)?
$300 A degree-3 polynomial has at most this many x-intercepts.
What is 3?
$300 At most, a graph may have this many number of turning points.
What is one less than the highest degree?
$400 In the polynomial 4x³ − 2x + 9, this is the leading coefficient.
What is 4?
$400 The product of (2x − 1)(3x² + x − 5).
What is 6x³ − x² − 11x + 5?
$400 Factor 3x² + 10x − 8.
What is (3x − 2)(x + 4)?
$400 If a zero has even multiplicity, the graph does this at that x-value.
What is touch/bounce (not cross) the x-axis?
$400 These are the three synonyms for "zeroes" discussed in class.
What are solutions, x-intercepts, and roots?
$500 This is the degree of the polynomial 6x⁵ − x³ + 2x − 11.
What is 5?
$500 Divide 4x³ − 8x² + 6x by 2x.
What is 2x² − 4x + 3?
$500 Factor x³ + 27 completely using sum of cubes.
What is (x + 3)(x² − 3x + 9)?
$500 The end behavior of −2x⁴ + 5x − 1: as x → ±∞, y → ___.
What is y → −∞ (falls on both ends)?
$500 This is the end behavior of a graph that has a negative leading coefficient and an odd degree.
What is up/down?