Chapter 6 Study Guide:
1) Find the degree of these functions: (6.1)
a) a2b
b) x-5yz6
c) x2 + 2x + 5
2) Add or Subtract, Simplify, then list the degree and leading coefficient (6.1)
a) (1 – x2) – (3x2 + 2x – 5)
b) (-x3 + 2x) – (-x3 + 2x – 7)
c) (6x5 – 2x) + (10x2 -15)
3) Multiply, Simplify, then list the degree and the leading coefficient (6.2)
a) (x3 + 3x + 4) (x – 2)
b) (x2 + 2x – 1) (x2 + 5)
4) Use long division to divide these polynomials: (6.3)
a) 2x2 + 7x + 7 ÷ x + 2
b) 5x3 + 2x2 -3x + 1 ÷ x + 1
5) Use synthetic division to divide these polynomials: (6.3)
a) 2x2 + 7x + 7 ÷ x + 2 (Check to see that you get the same answer)
b) 5x3 + 2x2 -3x + 1 ÷ x + 1 (Check to see that you get the same answer)
6) Use synthetic substitution (division) to solve for f(x) when x = 2 for this function: (6.3)
a) f(x) = 101x4 – 125x3 + 15x2 – 20x + 10 when x = 2
7) Factor these expressions (6.4)
a) Using SOAP: Factor x3 – 27
b) Using Grouping: x3 + 3x2 – 4x – 12
c) If x2 + x – 12 has a zero of x = -4 (use synthetic division)
8) Identify the possible real roots of this polynomial (6.5)
a) f(x) = x3 + 2x2 + x + 5
9) If given roots 7 and for a function, at minimum, how many roots are there?(6.6)
10) For these graphs of functions list 1)whether the polynomial is an even or odd degree, 2) if the leading coefficient is negative or not, 3) and the roots and their multiplicities. (6.7)
a)
b)
11) Write this polynomial p(x) = 2x3 - 14x2 + 3x + 10 after a
a) vertical translation up 1
b) horizontal translation to the left by 1
c) vertical stretch by 2
d) a reflection over the x-axis
e) a reflection over the y-axis