Polynomial Basics
Evaluate the following:
f(-3) for f(x)=
3x^3-2x^2+4x-1
f(-3)=
-112
Factor:
x^2-8x-9
(x-9)(x+1)
What is the y-intercept of
y=3x^3-5+2x-6x^2
(0-5)
What is the 2nd term in row 4 of Pascal's Triangle?
4
Classify (Name) the polynomial by degree and number of terms:
f(x)=2x^3+x-x^3+4
Cubic Trinomial
Factor:
x^3+20x^2+100x
x(x+10)(x+10)
Which direction(s) do the ends of the polynomial graph point?
y=-4x^4-3x^2+1
both ends point down
Factor:
x^3+64
(x+4)(x^2-4x+16)
Add and write in standard form:
(x^3-2x^2-8)+(2x^4+4x^2-x+3)
2x^4+x^3+2x^2-x-5
Factor:
x^3-5x^2-16x+80
(x-5)(x+4)(x-4)
What is the minimum and maximum points of the graph of
y=x^3-4x^2
Max: (0,0)
Min: (2.7, -9.5)
Combine like terms and write in standard form:
x^4+3x-2x^2-x^5+3x^4+3+x^5-4x^2+3-10x^3-5+7x^2
4x^4-10x^3+x^2+3x-2
Subtract and write in standard form:
(x^3+4x-5)-(2x^3+4x^2-x-6)
-x^3-4x^2+5x+1
Factor:
8x^3+1000
(2x+10)(4x^2-20x+100)
What are the x-intercepts of
y=x^3+4x^2-9x-36
(-4, 0), (3,0), & (-3,0)
Use the Binomial Theorem and Pascal's Triangle to expand:
(x+8)^5
x^5+40x^4+640x^3+5120x^2+20480x+32768
Multiply:
(x^2-4x+1)(2x^2-3x-2)
2x^4-11x^3+12x^2+5x-2
Factor:
2x^4-16x^2-18
2(x+3)(x-3)(x^2+1)
What are the x-intercepts of
y=x^5-18x^3+32x
(0,0), (1.4, 0), (-1.4,0), (4,0), & (-4,0)
Factor:
4x^4+8x^2+3
(2x^2+1)(2x^2+3)