Q. If a polynomial is expressed as P(x) = 2x^3 - 4x^2 + 3x - 5, what is the coefficient of x^2?
Show solution
Solution
In the polynomial P(x), the coefficient of x^2 is -4.
Correct Answer:
B
— -4
Learn More →
Q. If a polynomial is expressed as P(x) = 2x^3 - 4x^2 + 3x - 5, what is the coefficient of the x^2 term?
Show solution
Solution
In the polynomial P(x), the coefficient of the x^2 term is -4.
Correct Answer:
B
— -4
Learn More →
Q. If a polynomial p(x) is expressed as p(x) = x^2 - 5x + 6, what are its roots?
A.
2 and 3
B.
1 and 6
C.
0 and 6
D.
5 and 1
Show solution
Solution
The roots of the polynomial can be found by factoring it as (x - 2)(x - 3) = 0, giving roots 2 and 3.
Correct Answer:
A
— 2 and 3
Learn More →
Q. If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, what are its roots?
A.
2 and 3
B.
1 and 6
C.
0 and 6
D.
5 and 1
Show solution
Solution
The roots of the polynomial can be found by factoring it as (x - 2)(x - 3) = 0, giving roots 2 and 3.
Correct Answer:
A
— 2 and 3
Learn More →
Q. If a polynomial p(x) is given by p(x) = x^2 - 5x + 6, what are the roots of the polynomial?
A.
2 and 3
B.
1 and 6
C.
0 and 6
D.
5 and 1
Show solution
Solution
The roots of the polynomial can be found by factoring it as (x - 2)(x - 3) = 0, giving roots 2 and 3.
Correct Answer:
A
— 2 and 3
Learn More →
Q. If a polynomial p(x) is given by p(x) = x^3 - 6x^2 + 11x - 6, what can be inferred about its roots?
A.
It has three distinct real roots.
B.
It has one real root and two complex roots.
C.
It has no real roots.
D.
It has two distinct real roots.
Show solution
Solution
By applying the Rational Root Theorem and synthetic division, we can find that p(x) has three distinct real roots.
Correct Answer:
A
— It has three distinct real roots.
Learn More →
Q. If the polynomial f(x) = x^3 - 3x^2 + 4 is evaluated at x = 1, what is the result?
Show solution
Solution
Evaluating f(1) gives 1^3 - 3(1^2) + 4 = 1 - 3 + 4 = 2.
Correct Answer:
A
— 2
Learn More →
Q. If the polynomial f(x) = x^3 - 6x^2 + 11x - 6 is factored, which of the following is one of its factors?
A.
x - 1
B.
x + 2
C.
x - 3
D.
x + 1
Show solution
Solution
The polynomial can be factored as (x - 1)(x - 2)(x - 3), so x - 1 is one of its factors.
Correct Answer:
A
— x - 1
Learn More →
Q. If the polynomial f(x) = x^4 - 4x^3 + 6x^2 - 4x + 1 is evaluated at x = 1, what is the result?
Show solution
Solution
Substituting x = 1 into the polynomial gives f(1) = 1 - 4 + 6 - 4 + 1 = 0.
Correct Answer:
A
— 1
Learn More →
Q. If the polynomial f(x) = x^4 - 4x^3 + 6x^2 - 4x + 1, what can be inferred about its symmetry?
A.
It is symmetric about the y-axis.
B.
It is symmetric about the x-axis.
C.
It is symmetric about the origin.
D.
It is symmetric about the line x = 1.
Show solution
Solution
The polynomial can be rewritten in a form that shows symmetry about the line x = 1.
Correct Answer:
D
— It is symmetric about the line x = 1.
Learn More →
Q. If the polynomial g(x) = x^2 + bx + c has a double root, what can be inferred about its discriminant?
A.
It is greater than zero.
B.
It is less than zero.
C.
It is equal to zero.
D.
It can be any value.
Show solution
Solution
A polynomial has a double root when its discriminant is equal to zero.
Correct Answer:
C
— It is equal to zero.
Learn More →
Q. If the polynomial g(x) = x^2 + bx + c has roots -2 and 3, what is the value of b?
Show solution
Solution
Using Vieta's formulas, the sum of the roots (-2 + 3) = 1, which means b = -1.
Correct Answer:
C
— 5
Learn More →
Q. If the polynomial P(x) = x^2 + bx + c has roots 3 and -2, what is the value of b?
Show solution
Solution
Using Vieta's formulas, the sum of the roots (3 + (-2)) = 1, hence b = -1.
Correct Answer:
B
— 5
Learn More →
Q. If the polynomial P(x) = x^2 - 5x + 6 has roots r1 and r2, what is the value of r1 + r2?
Show solution
Solution
According to Vieta's formulas, the sum of the roots r1 + r2 of the polynomial x^2 - 5x + 6 is equal to the coefficient of x (which is -(-5)) = 5.
Correct Answer:
A
— 5
Learn More →
Q. If the polynomial P(x) = x^2 - 5x + 6 is factored, what are the roots of the polynomial?
A.
2 and 3
B.
1 and 6
C.
3 and 2
D.
0 and 5
Show solution
Solution
Factoring the polynomial gives (x - 2)(x - 3), so the roots are 2 and 3.
Correct Answer:
A
— 2 and 3
Learn More →
Q. If the polynomial P(x) = x^2 - 5x + 6 is factored, what are the roots?
A.
2 and 3
B.
1 and 6
C.
3 and 2
D.
0 and 6
Show solution
Solution
Factoring the polynomial P(x) gives (x - 2)(x - 3), so the roots are 2 and 3.
Correct Answer:
A
— 2 and 3
Learn More →
Q. If the polynomial P(x) = x^3 - 3x^2 + 4 has a local maximum at x = 1, what is the value of P(1)?
Show solution
Solution
Calculating P(1) gives 1^3 - 3(1^2) + 4 = 1 - 3 + 4 = 2.
Correct Answer:
A
— 2
Learn More →
Q. In polynomial long division, what is the first step when dividing 2x^3 + 3x^2 - x + 4 by x + 2?
A.
Divide the leading term of the dividend by the leading term of the divisor.
B.
Multiply the entire divisor by the first term of the quotient.
C.
Subtract the product from the dividend.
D.
Bring down the next term from the dividend.
Show solution
Solution
The first step in polynomial long division is to divide the leading term of the dividend by the leading term of the divisor.
Correct Answer:
A
— Divide the leading term of the dividend by the leading term of the divisor.
Learn More →
Q. In polynomial long division, what is the first step when dividing 4x^3 + 2x^2 - x by 2x?
A.
Divide the leading term of the dividend by the leading term of the divisor.
B.
Multiply the divisor by the leading term of the dividend.
C.
Subtract the product from the dividend.
D.
Write down the remainder.
Show solution
Solution
The first step in polynomial long division is to divide the leading term of the dividend by the leading term of the divisor.
Correct Answer:
A
— Divide the leading term of the dividend by the leading term of the divisor.
Learn More →
Q. In polynomial long division, what is the first step when dividing 4x^3 + 2x^2 - x by 2x + 1?
A.
Multiply the divisor by the leading term of the dividend.
B.
Subtract the product from the dividend.
C.
Identify the degree of both polynomials.
D.
Write the remainder.
Show solution
Solution
The first step in polynomial long division is to multiply the divisor by the leading term of the dividend.
Correct Answer:
A
— Multiply the divisor by the leading term of the dividend.
Learn More →
Q. In polynomial long division, what is the first step when dividing 4x^3 by 2x?
A.
Multiply 2x by 2x^2.
B.
Subtract 2x from 4x^3.
C.
Divide 4 by 2.
D.
Add the exponents.
Show solution
Solution
The first step in polynomial long division is to divide the leading term of the dividend by the leading term of the divisor, which in this case is 4x^3 ÷ 2x = 2x^2.
Correct Answer:
A
— Multiply 2x by 2x^2.
Learn More →
Q. In the context of polynomials, which of the following statements best describes the degree of a polynomial?
A.
It is the highest power of the variable in the polynomial.
B.
It is the number of terms in the polynomial.
C.
It is the sum of the coefficients of the polynomial.
D.
It is the product of the roots of the polynomial.
Show solution
Solution
The degree of a polynomial is defined as the highest power of the variable present in the polynomial.
Correct Answer:
A
— It is the highest power of the variable in the polynomial.
Learn More →
Q. In the polynomial 2x^3 + 3x^2 - x + 5, which term has the highest degree?
A.
2x^3
B.
3x^2
C.
-x
D.
5
Show solution
Solution
The term with the highest degree is 2x^3, as it has the highest exponent of x.
Correct Answer:
A
— 2x^3
Learn More →
Q. In the polynomial 4x^3 - 2x^2 + x - 5, what is the coefficient of x^2?
Show solution
Solution
The coefficient of x^2 in the polynomial 4x^3 - 2x^2 + x - 5 is -2.
Correct Answer:
B
— -2
Learn More →
Q. In the polynomial 5x^4 - 3x^3 + 2x^2 - x + 7, what is the coefficient of the x^2 term?
Show solution
Solution
The coefficient of the x^2 term in the polynomial is 2.
Correct Answer:
C
— 2
Learn More →
Q. In the polynomial expression 4x^3 - 2x^2 + x - 5, which term is the constant term?
A.
4x^3
B.
-2x^2
C.
x
D.
-5
Show solution
Solution
The constant term in a polynomial is the term that does not contain any variables, which in this case is -5.
Correct Answer:
D
— -5
Learn More →
Q. In the polynomial expression 4x^3 - 3x^2 + 2x - 1, which term is the constant term?
A.
4x^3
B.
-3x^2
C.
2x
D.
-1
Show solution
Solution
The constant term in a polynomial is the term that does not contain any variable, which in this case is -1.
Correct Answer:
D
— -1
Learn More →
Q. In the polynomial f(x) = 2x^3 - 3x^2 + x - 5, what is the coefficient of x^2?
Show solution
Solution
The coefficient of x^2 in the polynomial f(x) = 2x^3 - 3x^2 + x - 5 is -3.
Correct Answer:
B
— -3
Learn More →
Q. In the polynomial f(x) = 2x^4 - 3x^3 + x - 5, what is the coefficient of x^3?
Show solution
Solution
The coefficient of x^3 in the polynomial f(x) = 2x^4 - 3x^3 + x - 5 is -3.
Correct Answer:
A
— -3
Learn More →
Q. In the polynomial h(x) = 4x^3 - 2x^2 + 3, what is the constant term?
Show solution
Solution
The constant term in the polynomial h(x) = 4x^3 - 2x^2 + 3 is 3.
Correct Answer:
C
— 3
Learn More →
Showing 1 to 30 of 70 (3 Pages)
Polynomials MCQ & Objective Questions
Polynomials are a fundamental topic in mathematics that play a crucial role in various school and competitive exams. Understanding polynomials not only enhances your mathematical skills but also boosts your confidence in solving complex problems. Practicing MCQs and objective questions on polynomials is essential for effective exam preparation, as it helps you identify important questions and strengthens your grasp of key concepts.
What You Will Practise Here
Definition and types of polynomials
Polynomial operations: addition, subtraction, multiplication, and division
Factoring polynomials and finding roots
Polynomial equations and their solutions
Graphing polynomial functions and understanding their behavior
Applications of polynomials in real-life scenarios
Common theorems related to polynomials
Exam Relevance
Polynomials are a significant part of the curriculum for CBSE, State Boards, NEET, JEE, and other competitive exams. You can expect questions related to polynomial operations, factoring, and graphing in both objective and subjective formats. Common question patterns include solving polynomial equations, identifying the degree of polynomials, and applying the Remainder and Factor Theorems. Mastering these concepts will not only help you tackle direct questions but also enhance your problem-solving skills in higher-level mathematics.
Common Mistakes Students Make
Confusing the degree of a polynomial with its leading coefficient
Overlooking the importance of signs when adding or subtracting polynomials
Making errors in factoring polynomials, especially with quadratic expressions
Misinterpreting the roots of polynomials and their multiplicities
Neglecting to check for extraneous solutions in polynomial equations
FAQs
Question: What are polynomials?Answer: Polynomials are algebraic expressions that consist of variables raised to non-negative integer powers, combined using addition, subtraction, and multiplication.
Question: How can I improve my understanding of polynomials?Answer: Regular practice of polynomials MCQ questions and solving objective questions with answers will significantly enhance your understanding and retention of the topic.
Start your journey towards mastering polynomials today! Solve practice MCQs and test your understanding to ensure you are well-prepared for your exams. Remember, practice makes perfect!
