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Factoring Methods
Division
Find f(x) when x =...
Mixed Multiple Choice
Mixed Open-Ended
100
(a2+4)(a-2) when it is simplified.
What is a3 - 2a2 + 4a - 8?
100
Use Synthetic division to find the remainder when 2x5 + 3x4 + 25x2 − 1 is divided by x + 3.
What is −3?
100
f(-2) if f(x) = 3x2 – 2x – 6
What is 10?
100
If P(x) is a polynomial of odd degree with real coefficients, the the equation P(x) = 0 has... A. at least one real root B. no roots C. at most 2 real roots
A. at least one real root
100
f(x) = 2x2 – 3x + 4 -divide the polynomial by x – 2
f(2)=6
200
By grouping and by completing the square.
What are 2 ways to factor a polynomial?
200
True or False: Dividend = Remainder • Divisor + Quotient
What is False. Correct: Dividend = Quotient • Divisor + Remainder.
200
2g(-2a) if g(x) = 3x2 – 2x – 6
What is 24a2 + 8a – 12?
200
The function y = x(x+1)(x-2)2 has how many degrees? Also, does it have any double or triple roots? A. is a cubic function with a triple root at (0,-2) B. is a quartic function with a double root at (0,2) C. is a quintic function with a triple root at (0,-2) D. is a quintic function with a double root at (0,2)
B. is a quartic function with a double root at (0,2)
200
The binomial x – a is a factor of the polynomial f(x) if and only if...
f(a) = 0.
300
P(x) = anxn + an–1xn–1 + ... + a0 = 0
What is the Rational Root Theorem?
300
The remainder when x5 -2x3 +x2 -4 is divided by x-2.
What is 16?
300
p(2) when p(x) = x3 - 2x2 + 2x - 4
p(2) = 23 - 2(2)2 + 2(2) - 4 p(2) = 8 - 8 + 4 - 4 p(2) = 0
300
The graph of: p(x) = x2(x - 2)+ 2 will be A. Shifted down 2 units B. Stretched by a factor of 2 C. Shifted left 2 units D. Shifted right 2 units
D. Shifted right 2 units
300
f(x) = x5 + 4x4 – 2x3 – 4x2 + x – 1 What is the maximum amount of zeros this function can have?
5