Polynomial Operations
What is the result of adding the polynomials 3x2+4x−5 and x2−2x+3
What is 4x2+2x−2?
Find the points of intersection between the line y=2x+1 and the parabola y=x2+3x−4.
What are the points (−3,−5) and (1,3)?
What is the remainder when the polynomial 2x3+3x2−4x+5 is divided by x−1?
What is 6?
What is the end behavior of the polynomial f(x)=x3−3x2+2x−1?
What is "As x→∞, f(x)→∞, and as x→−∞, f(x)→−∞"?
Write the first five terms of the Fibonacci sequence starting with f(0)=1 and f(1)=1.
What are 1,1,2,3,5?
Multiply the polynomials 2x+3 and x2−x+4.
What is 2x3−2x2+8x+3x2−3x+12, which simplifies to 2x3+x2+5x+12?
Solve the system: y=x2−4x+3 and y=−x+1 graphically.
What are the points (1,0) and (3,−2)?
If x−2 is a factor of the polynomial 3x3−6x2+x−2, what is the remainder when the polynomial is divided by x−2?
What is 0?
Identify the relative maximum and minimum for the function f(x)=x2−4x+3.
What is the relative minimum at x=2, where f(2)=−1?
Write the first four terms of an arithmetic sequence with a common difference of 3, starting at 5.
What are 5,8,11,14?
If you subtract the polynomial x3−2x2+4x−5 from 3x3+x2−x+6, what is the result?
What is 2x3+3x2−5x+11?
Solve the system algebraically:
3x−2y=7
x2+y2=9
What is (3,−1) and (−1,5)?
According to the Remainder Theorem, if p(x)=x4−3x3+2x−5 , what is the remainder when divided by x−1?
What is p(1)=1−3+2−5=−5?
Sketch the graph of f(x)=−x2+4x−3 and identify the x-intercepts.
What is the x-intercepts are x=-1, -3?
Find the nth term formula for the geometric sequence: 2,6,18,54,…
What is an=2×3n-1 ?
Simplify the expression: (4x2+6x−8)+(−3x2+5x+7)−(2x2−x+4)
What is −x2+10x−5?
Graph the system of equations:
y=x2−2x
y=−x+2
What is the point of intersection?
What is (2,0)?
Using the Remainder Theorem, find the value of p(2) for the polynomial p(x)=x3−4x2+5x−6.
What is p(2) = 23−4(22)+5(2)−6 = 8−16+10−6 = −4?
Graph f(x)=2x3−3x2+5, and describe the behavior of the function at x=0.
What is "The graph has a y-intercept at (0, 5) and increases as x→∞ and decreases as x→−∞"?
Given the arithmetic sequence 4,7,10,… find the 10th term.
What is 4+(10−1)×3 = 4+27 = 31?
What is the result of multiplying (x+5)(x2−4x+3)?
What is x3−4x2+3x+5x2−20x+15, which simplifies to x3+x2−17x+15?
Find the points of intersection between the circle x2+y2=10 and the line y=2x−3.
What are the points (root(6), 2*root(6)-3) and (-root(6), -2*root(6)-3)?
If x+4 is a factor of x3−2x2−11x+20, what is the quotient after dividing the polynomial by x+4?
What is x2−6x+13-(32/(x+4))?
For the function f(x)=x4−4x2, identify its key features, including zeros, intervals of increase and decrease, and end behavior.
What is "The zeros are at x=−2,0,2, the function increases on (−2,0)and (0,2), decreases on (−∞,−2) and (2,∞), and the end behavior is f(x)→∞ as x→±∞"?
Given the arithmetic sequence 7,11,15,19,…, find the explicit formula for the nth term and use it to find the 15th term.
What is the explicit formula an=7+(n−1)×4 = 4n+3, and the 15th term is a15=4(15)+3=60+3=63?