Degree and Types of Polynomials
4y + 7
What is a first degree (linear) binomial
(3x+5) + (4x+1)
7x + 6
2x + 20
2(x + 10)
(x+2)(x+3)
x2+5x+6
These two types of exponents prevent an expression from being a polynomial.
What are negative and fractional exponents (roots)?
3x
What is a first degree (linear) monomial
(6x-7) + (4x+5)
10x-2
x2 + 11x + 18
(x + 2) (x + 9)
(x-7)(x+2)
x2-5x-14
The general case of (x + y)(x + y)
x2+2xy+y2
4x2 + 5x + 6
What is a second degree (quadratic) trinomial
(5x2-4x+7) - (8x2 -2x-2)
-3x2 -2x +9
x2 + 4x - 21
(x+7)(x-3)
(2x+4)(x-8)
2x2-12x-32
The GCF of 64x2y5+32x3y3+88xy4
8xy3(8xy2+4x2+11y)
We get this type of polynomial when we multiply (x+6)(x-8).
What is a quadratic trinomial?
Daily Double
(5x3+4x+7-x2) - (2x-6x2+x4)
-x4+5x3+5x2+2x+7
3x2-18x+27
3(x-3)(x-3)
(x-4)2
x2-8x+16
(4a+3)2
16a2 + 24a + 9
This type of polynomial is the result of the following product: (x+2)(x-2)
What is a quadratic binomial?
(3x3 + 3x2 – 4x + 5) + (x3 – 2x2 + x – 4)
4x3 + x2 – 3x + 1
3x2 + 11x + 6
(x+3)(3x+2)
DAILY DOUBLE (this one is HARD!) (2x2+3)(3x2 − 4x + 7)
6x4 − 8x3 + 23x2 − 12x + 21
Simplify and factor (Remember order of operations):
7x3 +8x2-10x3+9x+3x3-3x-6x2
2x(x+3)