Features of Polynomials
What is the constant in the equation below?
y=3x^2-5x+19
19
What is the y-intercept of the equation below?
y=6x^3-4x^2+7x+1
1
(the constant)
Fill in the blank:
x\cdot [_]=5x^3
The blank should be
5x^2
What is the degree of the polynomial below?
2x^8+7x^6-3x^5-x^3+9x^2-1
8
Both ends of a certain polynomial graph point up. What two things do we know about the polynomial equation, based on this end behavior?
1. The degree is even
2. The leading coefficient is positive
Use the distributive property to multiply:
2x(x-4)
2x^2-8x
Rewrite the polynomial in standard form
3x^4+9-2x^6+8x^3
-2x^6+3x^4+8x^3+9
The graph of the equation below touches (but does not cross) the x-axis at what x-intercept?
y=(x-4)^3(x+8)^2
x = -8
(because (x + 8) has an even exponent
Give an example of a polynomial that:
* decreases as x gets larger in the positive direction * increases as x gets larger in the negative direction.
Any polynomial that has an odd degree and negative leading coefficient