SAT Math : Polynomials
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Example Questions
Example Question #12 : Variables
Find the degree of the polynomial:
To find the degree of a polynomial we must find the largest exponent in the function.
The degree of the polynomial 
Example Question #1 : Polynomial Operations
What is the degree of the polynomial 
When a polynomial has more than one variable, we need to find the degree by adding the exponents of each variable in each term.Â
Example Question #3 : Polynomial Operations
Find the degree of the following polynomial:
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 
Example Question #1 : How To Find The Degree Of A Polynomial
Solve each problem and decide which is the best of the choices given.
Â
What is the degree of the following polynomial?
The degree is defined as the largest exponent in the polynomial. In this case, it is 
Example Question #1 : Polynomials
What is the degree of this polynomial?
Degree 6
Degree 12
Degree 10
Degree 7
Degree 8
Degree 8
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 #1 : Polynomials
Find the degree of the following polynomial:Â
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 
Example Question #1 : Polynomials
If 3 less than 15 is equal to 2x, then 24/x must be greater than
Â
3
6
4
5
3
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.Â
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Example Question #2 : 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
I and II
I, II and III
II & III
I and III
I only
I and III
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 #3 : Polynomials
If a positive integer a is divided by 7, the remainder is 4.  What is the remainder if 3a + 5 is divided by 3?
6
3
2
5
4
2
The best way to solve this problem is to plug in an appropriate value for a.  For example, plug-in 11 for a because 11 divided by 7 will give us a remainder of 4.Â
Then 3a + 5, where a = 11, gives us 38.  Then 38 divided by 3 gives a remainder of 2.
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The algebra method is as follows:
a divided by 7 gives us some positive integer b, with a remainder of 4.
Thus,
a / 7 = b 4/7
a / 7 = (7b + 4) / 7
a =Â (7b + 4)
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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 #4 : Polynomials
Â
Â
42
38
36
100
45
42
Â
 
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