Fill in the blank with either degree, conjugates, or polynomial.

Question

Fill in the blank with either degree, conjugates, or polynomial.

a. The standard form of a __________________ has terms written in descending order by degree.

b. The exponent of the variable in a term determines the ____________________ of the term?

c. The numbers a+bi are a complex ___________________ pair.

Answer 1

Hi Marwa. Thinking about the definitions of these terms should help you answer the question.

A polynomial is an expression made up of constants and variables, like 5x²+3x-2. Each term in the polynomial has a degree, which is determined by the exponent on the variable in that term. For example, the degree of 5x² is 2. The degree of -2 is 0 because this term does not have a variable. Normally you will see polynomials written with the terms in the order of decreasing degree. This is known as standard form. For example, the standard form of the polynomial 8x+3x³ is 3x³+8x.

It is possible for polynomials to have a complex term, which involves the imaginary number i. A complex conjugate is a pair of complex numbers, each with a real and an imaginary part. Both pairs in a complex conjugate have the same real part, but opposite imaginary parts. For example, 3+2i and 3-2i are complex conjugates of each other.

To answer your question, the blank is part a. is filled by "polynomial", part b. is filled by "degree", and part b. is filled by "conjugates".

Answer 2

a. polynomial

b. degree

c. conjugate

Answer 3

Add answer

a. The standard form of a polynomial _ has terms written in descending order by degree.

b. The exponent of the variable in a term determines the _degree___________________ of the term?

c. The numbers a+bi ( and a- bi) are a complex _conjugate__________________ pair.

For example: X ³ _{- X} ² _{+ 2 X - 2} Polynomial of degree three since the variable with the highest term has exponent three

( 1 +2 i) and (1 - 2i ) are complex conjugates

A polynomial may have complex roots . Complex roots always occur in pairs of a complex number and its conjugate.