All about Polynomials
What is the end behavior of the function?
x4-3x2+2x-5
Up and Up
Find the sum of the polynomials
(-6x2 + 3x -7) + (10x2+4x-2)
4x2+7x-9
Divide the polynomials using any method
(x2+x+12)÷ (x-5)
x+6+42/x-5
Factor the polynomial
x3 - x2 - 12x
x(x - 4)(x - 3)
Solve the polynomial equation
x3-x2-30x = 0
x = -5, x = 0, x = 6
What is the degree and leading coefficient of the polynomial?
2x2-3x6+5x4+2-3x3-22x5
Degree: 6
Leading Coefficient: -3
Find the difference of the polynomials
(4x3+6x2-9x+1) - (8x3+2x2-5x-1)
-4x3+4x2-4x+2
Divide the polynomials using synthetic division
(2x2-x-1)÷ (x-2)
2x + 3 + 5/(x-2)
Factor the polynomial
x3+27
(x + 3)(x2-3x+9)
Find all of the possible rational roots of the equation
6x3+2x2-4x+22
+-1, 2, 11, 22, 1/2, 11/2, 1/3, 2/3, 11/3, 22/3, 1/6, 11/6
Write the polynomial in standard form
4x2-3x+5x3-7
5x3+4x2-3x-7
Find the product
(8x2-3x+1)(-3x+2)
-24x3+25x2-9x+2
Divide the polynomials using long division
(x2+6x+1)÷ (x-3)
x + 9 + 28/(x-3)
Factor the polynomial
x3 - 3x2 + 4x - 12
(x - 3)(x2+4)
Write an equation given the roots
x = 2, x = 3i
f(x) = x3-2x2+9x-18
What type of polynomial is this?
x4-3x3+22x2-39x+24
Find the product
(2x+3)3
8x3+36x2+54x+27
Divide the polynomials using synthetic division:
(x3 - 9x + 12)÷ (x + 3)
x2 - 3x + 12/(x+3)
Factor the polynomial
36x4-25
(6x2-5)(6x2+5)
Find all of the roots of the equation
f(x) = x3+x2-5x+3
What kind of roots do you have?
x = 1, x = 1, x = -3
x = 1 is a double root, x = -3 is a single root
What is the end behavior of an odd degree function with a negative leading coefficient?
Up and Down
Find the product:
(3x2-6x-5)(x4+2x2+5x)
3x6-6x5+x4+3x3-40x2-25x
Divide the polynomials using long division
(x3+3x2 - 4x -6)÷(x2 - 4)
x + 3 + 6/(x2-4)
Is the binomial a factor of the polynomials?
f(x) = 3x3+7x2-8x-5
x + 5
No, the remainder does not = 0
Find all of the roots of the equation
f(x) = x4- 5x2 - 36
x = 3 and x = -3 are roots
x = 3, x = -3, x = 2i, x = -2i