All GED Math Resources
Example Questions
Example Question #1 :Algebra
Multiply:
Example Question #1 :Simplifying, Distributing, And Factoring
Factor:
where
The numbersandfit those criteria. Therefore,
You can double check the answer using the FOIL method
Example Question #3 :Algebra
Which of the following isnota prime factor of?
Factorall the way to its prime factorization.
can be factored as the difference of two perfect square terms as follows:
is a factor, and, as the sum of squares, it is a prime.is also a factor, but it is not aprimefactor - it can be factored as the difference of two perfect square terms. We continue:
Therefore, all of the given polynomials are factors of, butis the correct choice, as it is not aprimefactor.
Example Question #1 :Simplifying, Distributing, And Factoring
Which of the following is a prime factor of?
can be seen to fit the pattern
:
where
can be factored as, so
.
does not fit into any factorization pattern, so it is prime, and the above is the complete factorization of the polynomial. Therefore,is the correct choice.
Example Question #5 :Algebra
Divide:
Divide termwise:
Example Question #6 :Algebra
Multiply:
This product fits the difference of cubes pattern, where:
so
Example Question #7 :Algebra
Give the value ofthat makes the polynomialthe square of a linear binomial.
A quadratic trinomial is a perfect square if and only if takes the form
for some values ofand.
, so
and.
Forto be a perfect square, it must hold that
,
so. This is the correct choice.
Example Question #1 :Simplifying, Distributing, And Factoring
Which of the following is a factor of the polynomial?
Perhaps the easiest way to identify the factor is to take advantage of the factor theorem, which states thatis a factor of polynomialif and only if. We substitute 1, 2, 4, and 9 forin the polynomial to identify the factor.
:
:
:
:
Onlymakes the polynomial equal to 0, so among the choices, onlyis a factor.
Example Question #1 :Algebra
Which of the following is a prime factor of?
is the sum of two cubes:
As such, it can be factored using the pattern
where;
The first factor,as the sum of squares, is a prime.
We try to factor the second by noting that it is "quadratic-style" based on. and can be written as
;
we seek to factor it as
We want a pair of integers whose product is 1 and whose sum is. These integers do not exist, sois a prime.
is the prime factorization and the correct response is.
Example Question #1 :Single Variable Algebra
Which of the following is a factor of the polynomial
Perhaps the easiest way to identify the factor is to take advantage of the factor theorem, which states thatis a factor of polynomialif and only if. We substituteandforin the polynomial to identify the factor.
:
:
:
:
Onlymakes the polynomial equal to 0, so of the four choices, onlyis a factor of the polynomial.