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Test: Polynomials in One Variable - SAT MCQ


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15 Questions MCQ Test Mathematics for SAT - Test: Polynomials in One Variable

Test: Polynomials in One Variable for SAT 2024 is part of Mathematics for SAT preparation. The Test: Polynomials in One Variable questions and answers have been prepared according to the SAT exam syllabus.The Test: Polynomials in One Variable MCQs are made for SAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test: Polynomials in One Variable below.
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Test: Polynomials in One Variable - Question 1

(x - y)2 = __________

Detailed Solution for Test: Polynomials in One Variable - Question 1

We can write (x - y)2 as (x - y) * (x - y) = x- xy - yx + y2
= x- 2xy + y2.

Test: Polynomials in One Variable - Question 2

Which of the following is the coefficient of x in the polynomial 7x2 + 6x - 2?

Detailed Solution for Test: Polynomials in One Variable - Question 2

As per the observation made from the polynomial 7x2 + 6x - 2, x is being multiplied by the number 6. Therefore, it is hereby deduced that 6 is the coefficient of x in the polynomial 7x2 + 6x - 2. Furthermore, 7 cannot be the coefficient of x as it is being multiplied by x2

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Test: Polynomials in One Variable - Question 3

How many terms are there in a polynomial 5x+ 2x - 2?

Detailed Solution for Test: Polynomials in One Variable - Question 3

We can get number of terms by separating them by “+” or “” sign.
In the given polynomial 5x+ 2x - 2, if we separate expressions by “+” or “” sign, we get three separate terms as 5x2, 2x and 2.
Hence we can say that there are three terms in the polynomial 5x+ 2x - 2.

Test: Polynomials in One Variable - Question 4

Which of the following is the zero for the polynomial p(x) = -5x + 5?

Detailed Solution for Test: Polynomials in One Variable - Question 4

p(x) = -5x + 5
-5x+5 = 0
5 = 5x
x = 1

Test: Polynomials in One Variable - Question 5

Which of the following is the example of Trinomial?

Detailed Solution for Test: Polynomials in One Variable - Question 5

Polynomials only having three terms are called Trinomials.
Hence to find trinomial polynomial, we have to find polynomial which has three terms. We can see that 5x+ 2x - 2 has three terms namely 5x2, 2x and 2. Hence it is trinomial.
Similarly, polynomials only having one term are called Monomials and polynomials only having two terms are called Binomials.

Test: Polynomials in One Variable - Question 6

Which of the following is the zero for the polynomial p(x) = cx + d?

Detailed Solution for Test: Polynomials in One Variable - Question 6

If p(x) = cx + d and cx + d = 0, then cx = -d. Furthermore, the outcome is x = -d/c. Therefore, it is derived that the zero for the polynomial p(x) = cx + d is -d/c, in accordance with the value of x which is -d/c. 

Test: Polynomials in One Variable - Question 7

When t = 0, which of the following is the value of p(t) = 2 + t + 2t2 − t3?

Detailed Solution for Test: Polynomials in One Variable - Question 7

If t = 0, then p(t) = 2 + t + 2t2 + t3 would be p(0) = 2 + 0 + 2(0)2 + (0)2. Its further results in 2. Therefore, according to the derivation, an observation can be made that the value of p(t) = 2 + t + 2t2 + t3 would be 2 when t = 0.

Test: Polynomials in One Variable - Question 8

Which of the following is a binomial of degree 20?

Detailed Solution for Test: Polynomials in One Variable - Question 8

Any polynomial with two terms along with degree 20 is a binomial of degree 20. As per the observation made from the polynomial x20 + 1, the degree is one as it is the highest level in terms of variables. Furthermore, the polynomial has two terms x20 and 1. 

Test: Polynomials in One Variable - Question 9

Amongst the following, which is a constant polynomial?

Detailed Solution for Test: Polynomials in One Variable - Question 9

Since 3 = 3x0, 3 is to be a constant polynomial. On the other hand, 4x + 1 and 6x + 3 are linear polynomials. Furthermore, 2x2 is a quadratic polynomial. 

Test: Polynomials in One Variable - Question 10

What kind of polynomial is 1 + 3x?

Detailed Solution for Test: Polynomials in One Variable - Question 10

Any polynomial bearing degree one is a linear polynomial. As per the observation made from the polynomial 1 + 3x, the degree is one as it is the highest level in terms of variables. Therefore, the type of polynomial is linear in nature. 

Test: Polynomials in One Variable - Question 11

Which of the following is the zero for the polynomial f(x) = 2x + 7?

Detailed Solution for Test: Polynomials in One Variable - Question 11

If f(x) = 2x + 7 and 2x + 7 = 0, then 2x = -7. Furthermore, the outcome is x = -7/2. Therefore, it is derived that the zero for the polynomial f(x) = 2x + 7 is -7/2, in accordance with the value of x which is -7/2. 

Test: Polynomials in One Variable - Question 12

When x = -1, which of the following is the value of f(x) = 5x − 4x2 + 3?

Detailed Solution for Test: Polynomials in One Variable - Question 12

If x = -1, then f(x) = 5x − 4x2 + 3 would be f(-1) = 5(-1) − 4(-1)2 + 3. It further results in -5 - 4 + 3. Further calculation leads to the outcome as -6. Therefore, according to the derivation, an observation can be made that the value of f(x) = 5x − 4x2 + 3 would be -6 when x = -1.

Test: Polynomials in One Variable - Question 13

Which of the following is a quadratic polynomial?

Detailed Solution for Test: Polynomials in One Variable - Question 13

Since the degree at the highest level for the polynomial 2x2 + x - 1 is two according to variables, it is to be a quadratic polynomial. On the other hand, 7x + 3 is a linear polynomial. Furthermore, x + 3x3 + 1 is a polynomial that is cubic

Test: Polynomials in One Variable - Question 14

Which of the following is the value of 72 - 52?

Detailed Solution for Test: Polynomials in One Variable - Question 14

72 would mean 7 needs to be multiplied by 7. The outcome will be 49. 52 would mean 5 needs to be multiplied by 5. The outcome will be 24. Therefore, if 25 is subtracted from 49, the outcome will be 24. As a result, it is hereby deduced that 72 - 52 will be 24.

Test: Polynomials in One Variable - Question 15

What kind of polynomial is x – x3?

Detailed Solution for Test: Polynomials in One Variable - Question 15

Any polynomial bearing degree three is a cubic polynomial. As per the observation made from the polynomial x – x3, the degree is three as it is the highest level in terms of variables. Therefore, the type of polynomial is cubic. 

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