All GED Math Resources
Example Questions
Example Question #1 : Simplifying, Distributing, And Factoring
Multiply:
Example Question #2 : Simplifying, Distributing, And Factoring
Factor:
where
The numbers and
fit those criteria. Therefore,
You can double check the answer using the FOIL method
Example Question #2 : Algebra
Which of the following is not a prime factor of ?
Factor all 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 a prime factor - it can be factored as the difference of two perfect square terms. We continue:
Therefore, all of the given polynomials are factors of , but
is the correct choice, as it is not a prime factor.
Example Question #1 : Algebra
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 #1 : Single Variable Algebra
Divide:
Divide termwise:
Example Question #1 : Algebra
Multiply:
This product fits the difference of cubes pattern, where :
so
Example Question #7 : Simplifying, Distributing, And Factoring
Give the value of that makes the polynomial
the square of a linear binomial.
A quadratic trinomial is a perfect square if and only if takes the form
for some values of
and
.
, so
and
.
For to be a perfect square, it must hold that
,
so . This is the correct choice.
Example Question #1 : 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 that is a factor of polynomial
if and only if
. We substitute 1, 2, 4, and 9 for
in the polynomial to identify the factor.
:
:
:
:
Only makes the polynomial equal to 0, so among the choices, only
is a factor.
Example Question #5 : 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, so
is a prime.
is the prime factorization and the correct response is
.
Example Question #6 : 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 that is a factor of polynomial
if and only if
. We substitute
and
for
in the polynomial to identify the factor.
:
:
:
:
Only makes the polynomial equal to 0, so of the four choices, only
is a factor of the polynomial.
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