Basic Single-Variable Algebra - Math
Card 0 of 3848
Solve for 
.
Solve for
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Subtract 
on both sides.
Divide 
on both sides.
Since it's absolute value, we need to accept both positive and negative answers.
For all values 
, which of the following is equivalent to the expression above?
For all values 
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First, factor the numerator. We need factors that multiply to 
and add to 
.
We can plug the factored terms into the original expression.
Note that 
appears in both the numerator and the denominator. This allows us to cancel the terms.
This is our final answer.
First, factor the numerator. We need factors that multiply to
We can plug the factored terms into the original expression.
Note that
This is our final answer.
Simplify the expression.
Simplify the expression.
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Because we are only multiplying terms in the numerator, we can disregard the parentheses.
To combine like terms in the numerator, we add their exponents.
To combine like terms between the numerator and denominator, subtract the denominator exponent from the numerator exponent.
Remember that any negative exponents stay in the denominator.
Because we are only multiplying terms in the numerator, we can disregard the parentheses.
To combine like terms in the numerator, we add their exponents.
To combine like terms between the numerator and denominator, subtract the denominator exponent from the numerator exponent.
Remember that any negative exponents stay in the denominator.
Give the value of 
that makes the polynomial 
the square of a linear binomial.
Give the value of
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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.
A quadratic trinomial is a perfect square if and only if takes the form
For
so
Exponentiate:
Exponentiate:
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The difference of two terms can be cubed using the pattern
Where 
:
The difference of two terms can be cubed using the pattern
Where
How many of the following are prime factors of 
?
I) 
II) 
III) 
IV) 
How many of the following are prime factors of
I)
II)
III)
IV)
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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, of the given four choices, only is not a factor, so the correct response is three.
Factor
Therefore, of the given four choices, only
Factor:
Factor:
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This can be factored out as the cube of a difference, where 
:
Therefore,
This can be factored out as the cube of a difference, where
Therefore,
Simplify:
Simplify:
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To simplify, we begin by simplifying the numerator. When muliplying like bases with different exponents, their exponents are added.
For x: 
For y: 
For z: 
The numerator is now 
.
When dividing like bases, their exponents are subtracted.
For x: 
For y: 
For z: 
Thus, our answer is 
.
To simplify, we begin by simplifying the numerator. When muliplying like bases with different exponents, their exponents are added.
For x:
For y:
For z:
The numerator is now
When dividing like bases, their exponents are subtracted.
For x:
For y:
For z:
Thus, our answer is
Which of the following linear binomials is a factor of the polynomial 
?
Which of the following linear binomials is a factor of the polynomial
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By the factor theorem, a polynomial 
is divisible by the linear binomial 
if and only if 
. We can use this fact to test each of the binomials by evaluating the dividend for the appropriate value of 
.
: Evaluate the polynomial at 
:
: Evaluate the polynomial at 
:
: Evaluate the polynomial at 
:
: Evaluate the polynomial at 
:
: Evaluate the polynomial at 
:
The dividend assumes the value of 0 at 
, so of the choices given, 
is the factor.
By the factor theorem, a polynomial
The dividend assumes the value of 0 at
What is 
increased by 40%?
What is
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A number increased by 40% is equivalent to 100% of the number plus 40% of the number. This is taking 140% of the number, or, equivalently, multiplying it by 1.4.
Therefore, 
increased by 40% is 1.4 times this, or
A number increased by 40% is equivalent to 100% of the number plus 40% of the number. This is taking 140% of the number, or, equivalently, multiplying it by 1.4.
Therefore,
Simplify the expression:
Simplify the expression:
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To solve this problem, we first need to factor the numerator. We are looking for two numbers that multiply to equal -8 and sum to equal 2.
Now, we can write out our expression in fraction form.
Since we have the like term 
in the numerator and denominator, we can cancel them out of our expression.
Thus, our answer is 
.
To solve this problem, we first need to factor the numerator. We are looking for two numbers that multiply to equal -8 and sum to equal 2.
Now, we can write out our expression in fraction form.
Since we have the like term
Thus, our answer is
Which of the following is a prime factor of 
?
Which of the following is a prime factor of
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is the difference of two squares:
As such, it can be factored as follows:
The first factor is the sum of cubes and the second is the difference of cubes; each can be factored further:
Therefore,
Of the choices, 
appears in the prime factorization and is therefore the correct choice.
As such, it can be factored as follows:
The first factor is the sum of cubes and the second is the difference of cubes; each can be factored further:
Therefore,
Of the choices,
Decrease 
by 20%. Which of the following will this be equal to?
Decrease
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A number decreased by 20% is equivalent to 100% of the number minus 20% of the number. This is taking 80% of the number, or, equivalently, multiplying it by 0.8.
Therefore, 
decreased by 20% is 0.8 times this, or
A number decreased by 20% is equivalent to 100% of the number minus 20% of the number. This is taking 80% of the number, or, equivalently, multiplying it by 0.8.
Therefore,
Divide:
Divide:
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Divide termwise:
Divide termwise:
Decrease 
by 30%. Which of the following will this be equal to?
Decrease
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A number decreased by 30% is equivalent to 100% of the number minus 30% of the number. This is taking 70% of the number, or, equivalently, multiplying it by 0.7.
Therefore, 
decreased by 30% is 0.7 times this, or
A number decreased by 30% is equivalent to 100% of the number minus 30% of the number. This is taking 70% of the number, or, equivalently, multiplying it by 0.7.
Therefore,
The polynomial 
is divisible by the linear binomial 
. Evaluate 
.
The polynomial
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By the factor theorem, a polynomial 
is divisible by the linear binomial 
if and only if 
. Therefore, we want the value of 
that makes the polynomial equal to 0 when evaluated at 
.
By the factor theorem, a polynomial
Factor:
Factor:
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can be rewritten as 
and is therefore the sum of two cubes. As such, it can be factored using the pattern
where 
.
where
Exponentiate:
Exponentiate:
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Vertical multiplication is perhaps the easiest way to multiply trinomials.
Vertical multiplication is perhaps the easiest way to multiply trinomials.
Solve for 
.
Solve for
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To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.
Add 
on both sides. Since 
is greater than 
and is positive, our answer is positive. We treat as a normal subtraction.
Multiply 
on both sides.
To isolate the variable in the equation, perform the opposite operation to move all constants on one side of the equation and leaving the variable on the other side of the equation.
Add
Multiply
Factor completely:
Factor completely:
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The grouping technique works here:
The first factor is the difference of squares and can be factored further accordingly:
The grouping technique works here:
The first factor is the difference of squares and can be factored further accordingly: