All SAT Math Resources
Example Questions
Example Question #1 : How To Divide Polynomials
Simplify:
Cancel by subtracting the exponents of like terms:
Example Question #12 : Polynomials
Divide by .
It is not necessary to work a long division if you recognize as the sum of two perfect cube expressions:
A sum of cubes can be factored according to the pattern
,
so, setting ,
Therefore,
Example Question #374 : Algebra
By what expression can be multiplied to yield the product ?
Divide by by setting up a long division.
Divide the lead term of the dividend, , by that of the divisor, ; the result is
Enter that as the first term of the quotient. Multiply this by the divisor:
Subtract this from the dividend. This is shown in the figure below.
Repeat the process with the new difference:
Repeating:
The quotient - and the correct response - is .
Example Question #1 : How To Multiply Polynomials
and
What is ?
so we multiply the two function to get the answer. We use
Example Question #11 : Polynomials
Find the product:
Find the product:
Step 1: Use the distributive property.
Step 2: Combine like terms.
Example Question #12 : Polynomials
represents a positive quantity; represents a negative quantity.
Evaluate
The correct answer is not among the other choices.
The first two binomials are the difference and the sum of the same two expressions, which, when multiplied, yield the difference of their squares:
Again, a sum is multiplied by a difference to yield a difference of squares, which by the Power of a Power Property, is equal to:
, so by the Power of a Power Property,
Also, , so we can now substitute accordingly:
Note that the signs of and are actually irrelevant to the problem.
Example Question #14 : Polynomials
represents a positive quantity; represents a negative quantity.
Evaluate .
can be recognized as the pattern conforming to that of the difference of two perfect cubes:
Additionally, by way of the Power of a Power Property,
, making a square root of , or 625; since is positive, so is , so
.
Similarly, is a square root of , or 64; since is negative, so is (as an odd power of a negative number is negative), so
.
Therefore, substituting:
.
Example Question #2 : How To Multiply Polynomials
and represent positive quantities.
Evaluate .
can be recognized as the pattern conforming to that of the difference of two perfect cubes:
Additionally,
and is positive, so
Using the product of radicals property, we see that
and
and is positive, so
,
and
Substituting for and , then collecting the like radicals,
.
Example Question #13 : Polynomials
Simplify the following expression:
This is not a FOIL problem, as we are adding rather than multiplying the terms in parentheses.
Add like terms together:
has no like terms.
Combine these terms into one expression to find the answer: