7.1 Introduction to Polynomials
How many terms are in the following polynomial?
2x+x^2y^3+2x^2-6
4
What is the degree of the following monomial?
x^3y^5
8
5x+2+5x+1
10x+3
10x-5x
5x
(2x)(3x)
6x^2
(x+1)(x+1)
x^2+2x+1
What is the leading coefficient of the following polynomial?
3x^4-2x^3+4x
3
Is the following polynomial in standard form?
x^2+4x-5x^3
No, it should be
-5x^3+x^2+4x
(3x^2-x)+(3x^2+5x)
6x^2+4x
(4x^3-x^2)-(3x^3-x^2)
x^3
(6x^3y)(3x^2y)
18x^5y^2
(x+5)(x-3)
x^2+2x-15
Which two terms are like terms? Why?
5x^2y-2x+2y+x^2y^2+10x^2y+2xy
5x^2y and 10x^2y
What is the degree of the following polynomial?
xyz+2x^2yz+3xy^2z^3
6
(a^2+a+1)+(2a^2+2a+2)
3a^2+3a+3
(5x^2y+4xy)-(3xy+2x^2y)
3x^2y+xy
3x(x+1)
3x^2+3x
(3x^2-2x)(x+2)
3x^3+4x^2-4x
What would the leading coefficient be if the following polynomial was in standard form?
x^4+3x-x^5+5
-1
Which polynomial is in standard form?
a.
x+x^2+1
b.
x^2+6x-x^4
c.
75x+2x^2
d.
x^3+10x^2-5
d.
x^3+10x^2-5
(-3a^2+2+6a)+(-a+2a^2-3)
-a^2+5a-1
(3x-2x^2+1)-(-2x+2x^2-1)
-4x^2+5x+2
5x^2(x^3+2x^2+3)
5x^5+10x^4+15x^2
(x+1)(3x^2+x-1)
3x^3+4x^2-1
Which of the following statements is true about the following polynomial?
4y^4-5y^5+3y^3+y^2
a. The polynomial is in standard form.
b. The leading coefficient is 4.
c. This is a fourth degree polynomial.
d. There are four terms.
d. There are four terms.
Which of the following statements is false about the following polynomial?
3x^3y+4xy-x^3y^2
a. The polynomial is not in standard form.
b. The leading coefficient is -1 when in standard form.
c. This is a third degree polynomial.
d. There are three terms in this polynomial.
c. This is a third degree polynomial. This is a fifth degree polynomial.
(x^2y+3xy-x^3y)+(-x^3y-3xy+x^2y)
-2x^3y+2x^2y
(-3x^3y^3+xy^2-5xy)-(xy+xy^2-4x^3y^3)
x^3y^3-6xy
3ab^2(a^3b-2ab+4)
3a^4b^3-6a^2b^3+12ab^2
(x^2-1)(x^3+x^2+x)
x^5+x^4-x^2-x