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Polynomials Practice Questions

Matric (South Africa) · Matric Mathematics · 134 free MCQs with instant results and detailed explanations.

134
Total
34
Easy
77
Medium
23
Hard

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Sample Questions from Polynomials

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Q1
Easy
What is the degree of the polynomial 3x^4 - 5x^2 + 7?
A. 4
B. 2
C. 7
D. 3
Show Answer & Explanation
Correct Answer: A
The degree of a polynomial is determined by the highest power of the variable. Here, the highest power is 4 (from 3x^4), so the degree is 4.
Q2
Easy
Which of the following is a factor of the polynomial x^2 - 5x + 6?
A. (x - 2)
B. (x + 3)
C. (x - 3)
D. (x + 2)
Show Answer & Explanation
Correct Answer: C
The polynomial x^2 - 5x + 6 can be factored as (x - 2)(x - 3). Therefore, (x - 3) is a factor of this polynomial.
Q3
Easy
What is the degree of the polynomial 4x^3 - 2x^2 + 5?
A. 3
B. 2
C. 5
D. 1
Show Answer & Explanation
Correct Answer: A
The degree of a polynomial is the highest power of the variable. In 4x^3 - 2x^2 + 5, the highest power of x is 3, hence the degree is 3.
Q4
Medium
What is the degree of the polynomial 4x^3 - 2x^2 + 7x - 5?
A. 3
B. 2
C. 1
D. 4
Show Answer & Explanation
Correct Answer: A
The degree of a polynomial is determined by the highest exponent of the variable. Here, the highest exponent is 3, making the degree 3.
Q5
Medium
Which of the following is a factor of the polynomial x^2 - 5x + 6?
A. (x - 2)
B. (x + 3)
C. (x - 1)
D. (2x - 3)
Show Answer & Explanation
Correct Answer: A
To find the factors, we can factor the polynomial as (x - 2)(x - 3). Thus, (x - 2) is a factor.
Q6
Medium
Which polynomial represents the sum of (2x^2 + 3x - 5) and (4x^2 - 2x + 1)?
A. 6x^2 + x - 4
B. 6x^2 + 5x - 6
C. 2x^2 + x - 4
D. 6x^2 + 5x - 4
Show Answer & Explanation
Correct Answer: D
Adding the two polynomials, we combine like terms: (2x^2 + 4x^2) + (3x - 2x) + (-5 + 1) gives 6x^2 + 5x - 4.
Q7
Medium
What is the degree of the polynomial expression 4x^3 - 3x^2 + 7x - 5?
A. 3
B. 2
C. 1
D. 0
Show Answer & Explanation
Correct Answer: A
The degree of a polynomial is defined as the highest power of the variable in the expression. In this case, the term 4x^3 has the highest power, which is 3.
Q8
Hard
What is the remainder when the polynomial f(x) = 3x^4 - 5x^3 + 2x^2 - 7 is divided by x - 2?
A. -3
B. 9
C. 5
D. 7
Show Answer & Explanation
Correct Answer: B
Using the Remainder Theorem, the remainder of f(x) when divided by x - c is f(c). Here, f(2) = 3(2^4) - 5(2^3) + 2(2^2) - 7 = 48 - 40 + 8 - 7 = 9.
Q9
Hard
If the polynomial f(x) = x^3 - 6x^2 + 11x - 6 has roots a, b, and c, which of the following expressions represents the sum of the squares of the roots?
A. (a + b + c)^2 - 2(ab + bc + ac)
B. (abc)^2
C. 3(a + b + c)
D. ab + ac + bc
Show Answer & Explanation
Correct Answer: A
The formula for the sum of the squares of the roots is (a + b + c)^2 - 2(ab + ac + bc), which is derived from the identity (x + y + z)^2 = x^2 + y^2 + z^2 + 2(xy + xz + yz). Thus, option A is correct.
Q10
Hard
If the polynomial f(x) = x^3 - 6x^2 + 11x - 6 can be factored completely, what are the roots of this polynomial?
A. 1, 2, 3
B. 2, 3, 4
C. 0, 1, 2
D. 1, 2, 4
Show Answer & Explanation
Correct Answer: A
The polynomial can be factored as (x - 1)(x - 2)(x - 3), which means the roots are 1, 2, and 3. This can be verified by substituting each root back into the polynomial.

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Polynomials — Matric (South Africa) Matric Mathematics Practice Questions Online

This page contains 134 practice MCQs for the chapter Polynomials in Matric (South Africa) Matric Mathematics. The questions are organized by difficulty — 34 easy, 77 medium, 23 hard — so you can choose the right level for your preparation.

Every question includes a detailed explanation to help you understand the concept, not just memorize answers. Take a timed quiz to simulate exam conditions, or practice at your own pace with no time limit.