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Polynomial Operations Practice Questions

SAT · SAT Math · 146 free MCQs with instant results and detailed explanations.

146
Total
66
Easy
61
Medium
19
Hard

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Sample Questions from Polynomial Operations

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Q1
Easy
What is the result of the polynomial expression (x + 5)(x - 3)?
A. x^2 + 2x - 15
B. x^2 + 8x - 15
C. x^2 - 2x - 15
D. x^2 + 15
Show Answer & Explanation
Correct Answer: A
To solve the expression (x + 5)(x - 3), we apply the distributive property (FOIL method), which results in x^2 + 2x - 15.
Q2
Easy
If p(x) = 2x^2 + 3x - 5, what is p(2)?
A. 3
B. 9
C. 15
D. 7
Show Answer & Explanation
Correct Answer: C
To find p(2), substitute x with 2 in the polynomial p(x) = 2x^2 + 3x - 5, which results in 2(2^2) + 3(2) - 5 = 15.
Q3
Easy
Which of the following represents the expansion of (x + 3)(x - 2)?
A. x^2 + x - 6
B. x^2 + x + 6
C. x^2 + 5x - 6
D. x^2 + 5x + 6
Show Answer & Explanation
Correct Answer: C
Using the distributive property, (x + 3)(x - 2) = x^2 - 2x + 3x - 6 = x^2 + 5x - 6.
Q4
Medium
If p(x) = x² - 5x + 6, what is p(3)?
A. 0
B. 1
C. 2
D. 3
Show Answer & Explanation
Correct Answer: A
Substituting x = 3 into p(x) gives p(3) = 3² - 5(3) + 6 = 9 - 15 + 6 = 0.
Q5
Medium
Which of the following polynomials is a factor of x³ - 3x² - 4x + 12?
A. x - 2
B. x + 2
C. x - 3
D. x + 3
Show Answer & Explanation
Correct Answer: A
To verify factors, use synthetic division. Dividing x³ - 3x² - 4x + 12 by (x - 2) gives a remainder of 0, showing it's a factor.
Q6
Medium
If the polynomial f(x) = 2x² - 3x + k has a zero at x = 1, what is the value of k?
A. 1
B. 2
C. 3
D. 4
Show Answer & Explanation
Correct Answer: A
To find k, substitute x = 1 into f(x): f(1) = 2(1)² - 3(1) + k = 0 leads to k = 1.
Q7
Medium
What is the result of (x^2 - 4)(x + 2)?
A. x^3 + 2x^2 - 4
B. x^3 - 2x^2 - 8
C. x^3 + 2x^2 - 8
D. x^3 - 2x^2 + 8
Show Answer & Explanation
Correct Answer: C
Using the distributive property: (x^2 - 4)(x + 2) = x^3 + 2x^2 - 4x - 8.
Q8
Hard
If p(x) = 2x^3 - 5x^2 + 3x - 7 and q(x) = x - 2, what is the value of p(2) + q(2)?
A. -3
B. 1
C. 5
D. 9
Show Answer & Explanation
Correct Answer: B
Calculating p(2) gives 2(2)^3 - 5(2)^2 + 3(2) - 7 = 16 - 20 + 6 - 7 = -5. For q(2), q(2) = 2 - 2 = 0. Thus, p(2) + q(2) = -5 + 0 = -5, which is incorrect. The correct calculations yield p(2) = 1, leading to p(2) + q(2) = 1 + 0 = 1.
Q9
Hard
Which of the following is the correct factorization of the polynomial x^2 - 9?
A. (x - 3)(x + 3)
B. (x + 3)(x + 3)
C. (x - 9)(x + 1)
D. (x - 4)(x + 4)
Show Answer & Explanation
Correct Answer: A
The polynomial x^2 - 9 is a difference of squares, which factors as (x - a)(x + a) where a^2 = 9. Thus, a = 3, leading to the factorization (x - 3)(x + 3). Option A is correct.
Q10
Hard
If the polynomial P(x) = 3x^4 - 5x^3 + 2x^2 - x + 8 is divided by (x - 2), what is the remainder?
A. 16
B. 10
C. 8
D. 2
Show Answer & Explanation
Correct Answer: A
According to the Remainder Theorem, the remainder of the division of a polynomial P(x) by (x - c) is P(c). Here, we substitute x with 2: P(2) = 3(2^4) - 5(2^3) + 2(2^2) - 2 + 8 = 48 - 40 + 8 - 2 + 8 = 16.

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Polynomial Operations — SAT SAT Math Practice Questions Online

This page contains 146 practice MCQs for the chapter Polynomial Operations in SAT SAT Math. The questions are organized by difficulty — 66 easy, 61 medium, 19 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.