SAT Math : Polynomial Operations

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #1 : Polynomial Operations

Find the degree of the polynomial:

Possible Answers:

Correct answer:

Explanation:

To find the degree of a polynomial we must find the largest exponent in the function.

The degree of the polynomial  is 5, as the largest exponent of  is 5 in the second term. 

Example Question #2 : Polynomial Operations

What is the degree of the polynomial ?

Possible Answers:

Correct answer:

Explanation:

When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term. 

 has a degree of 4 (since both exponents add up to 4), so the polynomial has a degree of 4 as this term has the highest degree. 

Example Question #3 : Polynomial Operations

Find the degree of the following polynomial:

Possible Answers:

Correct answer:

Explanation:

When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term.

Even though  has a degree of 5, it is not the highest degree in the polynomial - 

 has a degree of 6 (with exponents 1, 2, and 3). Therefore, the degree of the polynomial is 6.  

Example Question #4 : Polynomial Operations

Solve each problem and decide which is the best of the choices given.

 

What is the degree of the following polynomial?

Possible Answers:

Correct answer:

Explanation:

The degree is defined as the largest exponent in the polynomial. In this case, it is .

Example Question #5 : Polynomial Operations

What is the degree of this polynomial?

Possible Answers:

Degree 10

Degree 6

Degree 12

Degree 7

Degree 8

Correct answer:

Degree 8

Explanation:

When an exponent with a power is raised to another power, the value of the power are multiplied.

When multiplying exponents you add the powers together

The degree of a polynomial is the determined by the highest power. In this problem the highest power is 8.

Example Question #6 : Polynomial Operations

Find the degree of the following polynomial: 

Possible Answers:

Correct answer:

Explanation:

The degree of a polynomial is the largest exponent on one of its variables (for a single variable), or the largest sum of exponents on variables in a single term (for multiple variables).

Here, the term with the largest exponent is , so the degree of the whole polynomial is 6.

Example Question #1 : Polynomials

If 3 less than 15 is equal to 2x, then 24/x must be greater than

 

Possible Answers:

5

3

4

6

Correct answer:

3

Explanation:

Set up an equation for the sentence: 15 – 3 = 2x and solve for x.  X equals 6. If you plug in 6 for x in the expression 24/x, you get 24/6 = 4. 4 is only choice greater than a. 

 

 

Example Question #1 : Polynomials

Given a♦b = (a+b)/(a-b) and b♦a = (b+a)/(b-a), which of the following statement(s) is(are) true:

I. a♦b = -(b♦a)

II. (a♦b)(b♦a) = (a♦b)2

III. a♦b + b♦a = 0

Possible Answers:

I and II

I and III

II & III

I, II and III

I only

Correct answer:

I and III

Explanation:

Notice that - (a-b) = b-a, so statement I & III are true after substituting the expression. Substitute the expression for statement II gives ((a+b)/(a-b))((a+b)/(b-a))=((a+b)(b+a))/((-1)(a-b)(a-b))=-1 〖(a+b)〗2/〖(a-b)〗2 =-((a+b)/(a-b))2 = -(a♦b)2 ≠ (a♦b)2

Example Question #2151 : Sat Mathematics

If a positive integer a is divided by 7, the remainder is 4.  What is the remainder if 3a + 5 is divided by 3?

Possible Answers:

5

6

4

2

3

Correct answer:

2

Explanation:

The best way to solve this problem is to plug in an appropriate value for a.  For example, plug-in 11 for because 11 divided by 7 will give us a remainder of 4. 

Then 3a + 5, where = 11, gives us 38.  Then 38 divided by 3 gives a remainder of 2.

 

The algebra method is as follows:

a divided by 7 gives us some positive integer b, with a remainder of 4.

Thus,

/ 7 = b  4/7

/ 7 = (7b + 4) / 7

a = (7b + 4)

 

then 3a + 5 = 3 (7+ 4) + 5

(3a+5)/3 = [3(7+ 4) + 5] / 3

= (7+ 4) + 5/3

The first half of this expression (7b + 4) is a positive integer, but the second half of this expression (5/3) gives us a remainder of 2.

Example Question #1 : Polynomials

 

 

Polydivision1

Possible Answers:

42

100

36

38

45

Correct answer:

42

Explanation:

Polydivision2

 

 Polydivision4

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