Test: Introduction To Polynomials

x²+ 5x - 6 = 0
x² - x + 6x - 6
x (x-1) + 6 (x-1)
(x-1) (x+6)
x = 1; x = -6

3^3+5^3-8^3=27+125-512

=152-512

=-360

⇒ x²+ 5x - 6 = 0

⇒ x²+ 6x -x - 6 = 0

⇒ x(x+6) -1(x+6) = 0

⇒ (x-1) (x+6) = 0

⇒ x = 1, -6

use factor theorem as x+2 is factor of

x³-2ax²+16 so put x = -2 and equate the equation to 0

so putting x = -2

(-2)³-2a(-2)²+16 =0

-8-8a+16=0

-8a = -8

a = 8/8= 1

So,

a = 1

p(x) = ax
p(x) = 0
ax = 0
x = 0/a
x = 0
{0 by something is equals to 0}
Therefore,0 is the zero of the polynomial. 
Checking:-
p(0) = a(0)
= 0

p(-2) = 7 - 3(-2) + 2(-2)²

         = 7+6+8 = 21

A linear polynomial has 1 zero.

A quadratic polynomial has 2 zeroes.

A cubic polynomial has 3 zeroes.

In general, any polynomial has as many zeroes as its degree.

A cubic polynomial is a polynomial of degree 3. A univariate cubic polynomial has the form An equation involving a cubic polynomial is called a cubic equation. A closed-form solution known as the cubic formula exists for the solutions of an arbitrary cubic equation.

A zero polynomial is a polynomial in which all the coefficients are 0.

Let the polynomials highest power variable be x^n as per the above statement x^n = 0 

Now, The degree of the zero polynomial is log0 which is undefined. 

Hence. The degree of zero polynomial is undefined.

Zero of the zero polynomial is any real number.
e.g., Let us consider zero polynomial be 0(x-k), where k is a real number For determining the zero, put x-k = 0 ⇒ x = k Hence, zero of the zero polynomial be any real number. 

The degree refers to the highest power of the polynomial. In this polynomial X has highest power 4.So the degree of polynomial is 4.