GED Math : Single-Variable Algebra
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Example Questions
Example Question #31 : Simplifying, Distributing, And Factoring
Factor completely:
The polynomial is the difference of squares and can be factored using the pattern
where
as seen here:
Example Question #31 : Simplifying, Distributing, And Factoring
Which of the following is a factor of the polynomial 
The greatest common factor of the two terms is the monomial term 
Of the four choices, 
Example Question #32 : Simplifying, Distributing, And Factoring
Which of the following is a factor of the polynomial
The greatest common factor of the two terms is the monomial term
Of the four choices,
Example Question #31 : Single Variable Algebra
Simplify:
Raise a fraction to a negative power by raising its reciprocal to the power of the absolute value of the exponent. Then apply the power of a quotient rule:
Example Question #32 : Single Variable Algebra
Simplify:
To raise a number to a negative exponent, raise it to the absolute value of that exponent, then take its reciprocal. We do this, then apply the various properties of exponents:
Example Question #591 : Ged Math
Factor completely:
For a quadratic trinomial with a quadratic coefficient other than 1, use the factoring by grouping method.
First, find two integers whose product is 
Split the linear term accordingly, then factor by grouping, as follows.
Example Question #33 : Simplifying, Distributing, And Factoring
Factor:
The greatest common factor of the terms is 
The trinomial might be able to be factored as
where 
By trial and error, we find that
so the factorization becomes
Example Question #33 : Algebra
Decrease 
A number decreased by 40% is equivalent to 100% of the number minus 40% of the number. This is taking 60% of the number, or, equivalently, multiplying it by 0.6.
Therefore, 
Example Question #34 : Algebra
Increase 
A number increased by 20% is equivalent to 100% of the number plus 20% of the number. This is taking 120% of the number, or, equivalently, multiplying it by 1.2.
Therefore, 
Example Question #593 : Ged Math
Which of the following is a prime factor of 
This can be most easily solved by first substituting 
This becomes quadratic in the new variable, and can be factored as
filling out the blanks with two numbers whose sum is 
Therefore, after factoring and substituting back,
The first factor, the sum of squares, is prime. The second factors as the difference of squares, so the final factorization is
Of the choices given, 
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