#1
What is the degree of the polynomial 3x^2 - 5x + 2?
2
ExplanationDegree represents the highest power of the variable, which is 2 in this polynomial.
#2
Which of the following is not a polynomial?
√x + 3
ExplanationThe term with a square root is not a polynomial since it involves a radical expression.
#3
Which of the following is the factor theorem?
If a polynomial f(x) is divided by (x - a), the remainder is f(a).
ExplanationThe theorem states the relationship between factors and roots of a polynomial.
#4
Which of the following represents a difference of two squares?
x^2 - 25
ExplanationThis is in the form of (a^2 - b^2), where a and b are squared terms.
#5
Which of the following is a factor of the polynomial x^3 + 2x^2 - x - 2?
x - 1
ExplanationUsing synthetic division or polynomial division, x - 1 is found to be a factor.
#6
What is the result of the operation (x^2 + 3x - 4) + (2x^2 - 5x + 6)?
3x^2 - 2x + 2
ExplanationCombine like terms to get the result.
#7
What is the degree of the polynomial (x + 1)(x - 2)(x + 3)?
3
ExplanationThe degree is determined by the highest power of the variable, which is 3.
#8
Which of the following is a factor of the polynomial x^3 - 8x^2 + 17x - 10?
x - 1
ExplanationUsing synthetic division or polynomial division, x - 1 is found to be a factor.
#9
What is the sum of the roots of the polynomial equation x^2 - 6x + 9 = 0?
3
ExplanationThe sum of the roots can be found using Vieta's formulas, which is 3.
#10
Which of the following is a solution to the equation 2x^2 - 5x + 3 = 0?
x = 3, x = -1/2
ExplanationSolve the quadratic equation to find the roots.
#11
What is the remainder when the polynomial 3x^3 - 5x^2 + 2x + 7 is divided by x - 2?
11
ExplanationUse polynomial long division to find the remainder, which is 11.
#12
Which of the following is a solution to the equation x^3 - 5x^2 + 4x + 6 = 0?
-2
ExplanationSubstitute -2 into the equation to check for solution.
#13
What is the product of the roots of the polynomial equation 2x^2 + 5x - 3 = 0?
-3
ExplanationThe product of roots is equal to the constant term divided by the leading coefficient.
#14
What is the quotient when (3x^4 - 7x^3 + 2x^2 - 5x + 9) is divided by (x - 3)?
3x^3 - 16x^2 + 50x - 153
ExplanationPerform polynomial long division to find the quotient.
#15
What is the product of the roots of the equation x^2 - 9 = 0?
9
ExplanationBy Vieta's formulas, the product of roots is equal to the constant term.