Factoring Polynomials
Factor the polynomial:
x3+7x2+10x
x(x+5)(x+2)
Use Synthetic Division to divide the following equation:
(x2-3x-40)/ (x+5)
x-8
Divide the polynomial by long division.
(3x2+7x-20) / (x+4)
3x-5
Use the Box Method to solve the following equation:
(18x2+30x-72)/(6x+18)
3x-4
The term that determines a polynomial's end behavior.
What is the leading term (or leading coefficient and degree)?
Factor the polynomial:
9x3+6x2-3x
3x(3x-1)(x+1)
Use Synthetic Division to solve the following equation:
(x3+3x2-x+2)/(x-1)
x2+4x+3, R:5
Use Long Division to solve the following equation:
2x3-3x2-18x-8) / (x-4)
2x2+5x+2
Use the Box Method to solve the following equation:
(5x4-15x3+39x2-12x+28)/(5x2+4)
x2-3x+7
If the degree is even and the leading coefficient is positive, both ends of the graph go this direction.
What is up? (Both ends rise.)
Factor the polynomial:
3x3+12x2-3x-12
(3x2-3)(x+4)
Use Synthetic Division to solve the following equation:
(x3+27) / (x+3)
x2-3x+9
Use Long Division to solve the following equation:
(x2-7x+10)/ (x+3)
x-10, R:40
Use the Box Method to solve the following equation:
(3x4+27x3-2x2-45x-5)/(x2+9x+1)
3x2-5
A polynomial has a negative leading coefficient and an odd degree. Describe its end behavior.
What is left end up, right end down?
Factor the polynomial.
12x3+60x2+75x
3x(2x+5)(2x+5)
Use Synthetic Division to solve the following equation:
(x4+3x3+x+4) / (x+3)
x3-3x2+12x-35, R:109
Use Long Division to solve the following equation:
(x3+5x2-3x-1) / (x-1)
x2+6x+3, R:2
Use the Box Method to solve the following equation:
(6x3-6x2-8x)/(x-1)
6x2-8, R:-8
The graph of a polynomial falls to the left and rises to the right. Describe the degree and the sign of the leading coefficient.
What is an odd degree with a positive leading coefficient?
Factor the polynomial.
6x3+3x2+8x+4
(3x2+4)(2x+1)
Use Synthetic Division to solve the following equation:
(x5+1) / (x+1)
x4-x3+x2-x+1
Use Long Division to solve the following equation:
(2x2+x-7) / (x-5)
2x+11, R:48
Use the Box Method to solve the following equation:
(6x4+15x3-28x-6)/(x+2)
6x3+3x2-6x-16, R:26
Explain how the degree and sign of the leading coefficient work together to determine end behavior.
What is: The degree (odd/even) decides whether ends go in same of opposite directions, and the sign (positive/negative) decides which direction (up or down).