Polynomials - PSAT Math

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.

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

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.

Then 3_a + 5_, where a = 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,

a / 7 = b 4/7

a / 7 = (7_b +_ 4) / 7

a = (7_b_ + 4)

then 3_a + 5 =_ 3 (7_b_ + 4) + 5

(3_a_+5)/3 = \[3(7_b_ + 4) + 5\] / 3

= (7_b_ + 4) + 5/3

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

Cancel by subtracting the exponents of like terms:

By the remainder theorem, if a polynomial is divided by the linear binomial , the remainder is - that is, the polynomial evaluated at . The remainder of dividing by is the dividend evaluated at , which is

The degree of the polynomial is the largest degree of any one of it's individual terms.

The degree of is

The degree of is

The degree of is

The degree of is

The degree of is

is the largest degree of any one of the terms of the polynomial, and so the degree of the polynomial is .

The polynomial has one term, so its degree is the sum of the exponents of the variables:

The degree of a polynomial in more than one variable is the greatest degree of any of the terms; the degree of a term is the sum of the exponents. The degrees of the terms in the given polynomial are:

The degree of the polynomial is the greatest of these degrees, 100.

The degree of a polynomial in one variable is the greatest exponent of any of the powers of the variable. The terms have as their exponents, in order, 44, 20, 10, and 100; the greatest of these is 100, which is the degree.

The degree of a polynomial in one variable is the greatest exponent of any of the powers of the variable. The terms have as their exponents, in order, 10, 20, 30, and 40; 40 is the greatest of them and is the degree of the polynomial.

The degree of a polynomial is the highest degree of any term; the degree of a term is the exponent of its variable or the sum of the exponents of its variables, with unwritten exponents being equal to 1. For each term in a polynomial, write the exponent or add the exponents; the greatest number is its degree. We do this with all four choices:

:

A constant term has degree 0.

The degree of this polynomial is 5.

The degree of this polynomial is 5.

The degree of this polynomial is 5.

The degree of this polynomial is 5.

All four polynomials have the same degree.

The degree of a monomial term is the sum of the exponents of its variables, with the default being 1.

For each monomial, this sum - and the degree - is as follows:

:

:

: (note - 999 is the coefficient)

:

is the correct choice.

so we multiply the two function to get the answer. We use

This product fits the sum of cubes pattern, where :

So

Step 1: Distribute the negative to the second polynomial:

Step 2: Combine like terms:

Factor the expression

numerator: find two numbers that add to 2 and multiply to -8 \[use 4,-2\]

denominator: find two numbers that add to 5 and multiply to -14 \[use 7,-2\]

new expression:

Cancel the and cross multiply.

By multiplying with the foil method, we multiply our first values giving , our outside values giving . our inside values which gives , and out last values giving .

If the expression is expanded, then by the binomial theorem, the term is

or, equivalently, the coefficient of is

Therefore, the coefficient can be determined by setting