Polynomials

Question 1

Terms

Answer 1

An equation consisting of both a number and a variable.
Example:
3x^2 -> in this case, x is the variable, and 3 is the number. We can also have just x, since we can have 1x^1 = x, and we can have just 5, since 5x^0 = 5.

Question 2

Polynomial

Answer 2

A polynomial is multiple terms either added or subtracted together. This can be represented as 3x^2 + 2x^3.

Question 3

Identity

Answer 3

p(x) = x^2 - 2 would be an example. Simply put, a polynomial which has a solution x.

Question 4

Root

Answer 4

What makes the polynomial, or identity, 0. For example, we could have p(x) = x^2 - 2, in which the root would be √2.

Question 5

Coefficient

Answer 5

The “number” in the term.

Question 6

Scalar Multiplication

Answer 6

We get the value alpha and multiply every coefficient (Ck) by a (alpha).

Question 7

Degree of a Term

Answer 7

The degree of a term is all of the powers of a term added together.

Question 8

Degree of a Polynomial

Answer 8

The degree of a polynomial is the highest power of all the terms in the polynomial.

Question 9

Addition of polynomials

Answer 9

Add matching coefficients ; p(x) + q(x)

Question 10

Multiplication of polynomials

Answer 10

Multiplying the two polynomials p(x) and q(x) will give a degree of m + n, which is their own degrees respectively.