#1
What is the degree of the polynomial 3x^2 - 5x + 2?
2
ExplanationThe degree is the highest power of the variable in the polynomial.
#2
Which of the following is a binomial?
2x - 1
ExplanationA binomial is a polynomial with two terms.
#3
What is the leading coefficient of the polynomial 4x^3 + 2x^2 - 5x + 1?
4
ExplanationIt's the coefficient of the term with the highest power of x.
#4
Which of the following is a trinomial?
3x^4 + 2x^3 - 5x
ExplanationA trinomial is a polynomial with three terms.
#5
What is the constant term of the polynomial 2x^3 - 3x^2 + 4x - 5?
-5
ExplanationIt's the term without any x, i.e., the term with x^0.
#6
Which of the following is a monomial?
5x
ExplanationA monomial is a polynomial with only one term.
#7
What is the leading term of the polynomial 6x^5 - 3x^3 + 2x^2 - 4x + 1?
6x^5
ExplanationIt's the term with the highest degree.
#8
What is the result of dividing (x^3 - 6x^2 + 11x - 6) by (x - 3)?
x^2 - 3x + 2
ExplanationThis is the result obtained using polynomial long division.
#9
What is the sum of all the roots of the polynomial x^3 - 5x^2 + 6x?
5
ExplanationIt's determined by Vieta's formulas for cubic equations.
#10
What is the result of dividing (2x^4 - 7x^3 + 3x^2 - 5x + 4) by (x - 2)?
2x^3 - 11x^2 + 20x - 36
ExplanationResult of polynomial division using synthetic division or long division.
#11
What is the sum of all the roots of the polynomial 2x^4 - 3x^3 + 5x^2 - 7x + 1?
-3
ExplanationDetermined by Vieta's formulas for quartic equations.
#12
What is the result of dividing (3x^4 + 2x^3 - 5x^2 + 7x - 1) by (x - 1)?
3x^3 + 2x^2 - 5x + 1
ExplanationObtained through polynomial division.
#13
What is the sum of all the roots of the polynomial x^4 - 3x^3 + 2x^2 - 5x + 1?
-3
ExplanationFound using Vieta's formulas.
#14
What is the result of dividing (4x^5 + 3x^4 - 2x^3 + x^2 - 5x + 1) by (x - 2)?
4x^4 + 11x^3 + 19x^2 + 39x + 41
ExplanationResult obtained through polynomial long division.
#15
What is the remainder when x^4 + 3x^3 - 4x^2 + 2x - 7 is divided by x - 1?
7
ExplanationThe remainder is found using polynomial division.
#16
What is the remainder when x^5 + 2x^4 - 3x^3 + 4x^2 - 5x + 6 is divided by x - 2?
12
ExplanationCalculated using polynomial long division.
#17
What is the remainder when x^6 - 5x^5 + 4x^4 - 3x^3 + 2x^2 - x + 1 is divided by x - 1?
7
ExplanationCalculated using polynomial long division or synthetic division.
#18
What is the remainder when x^7 + 2x^6 - 3x^5 + 4x^4 - 5x^3 + 6x^2 - 7x + 8 is divided by x - 1?
13
ExplanationCalculated using polynomial long division or synthetic division.
#19
What is the remainder when x^8 - 4x^7 + 2x^6 - 3x^5 + 5x^4 - 2x^3 + 4x^2 - 3x + 1 is divided by x - 1?
5
ExplanationCalculated using polynomial long division or synthetic division.