SAT Math : Polynomials

Study concepts, example questions & explanations for SAT Math

varsity tutors app store varsity tutors android store varsity tutors amazon store varsity tutors ibooks store

Example Questions

← Previous 1 3 4

Example Question #1 :How To Find The Degree Of A Polynomial

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 polynomialis 5, as the largest exponent ofis 5 in the second term.

Example Question #2 :How To Find The Degree Of A Polynomial

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 :How To Find The Degree Of A Polynomial

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 thoughhas 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 :How To Find The Degree Of A Polynomial

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 #1 :How To Find The Degree Of A Polynomial

What is the degree of this polynomial?

Possible Answers:

Degree 10

Degree 6

Degree 7

Degree 8

Degree 12

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

多项式的次数是由the highest power. In this problem the highest power is 8.

Example Question #2 :How To Find The Degree Of A Polynomial

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 :Polynomial Operations

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

Possible Answers:

5

3

6

4

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 get24/6 = 4. 4 is only choice greater than a.

Example Question #1 :How To Divide 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:

II & III

I only

I and II

I, II and III

I and III

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 #1 :Polynomials

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

Possible Answers:

5

4

2

3

6

Correct answer:

2

Explanation:

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

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

The algebra method is as follows:

adivided by 7 gives us some positive integerb,with a remainder of 4.

Thus,

a/ 7 =b4/7

a/ 7 = (7b +4) / 7

a =(7b+ 4)

then 3a + 5 =3 (7b+ 4)+ 5

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

= (7b+ 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:

38

100

45

42

36

Correct answer:

42

Explanation:

Polydivision2

Polydivision4

← Previous 1 3 4
Learning Tools by Varsity Tutors