### All SAT Math Resources

## Example Questions

### Example Question #11 : Polynomials

and

What is ?

**Possible Answers:**

**Correct answer:**

so we multiply the two function to get the answer. We use

### Example Question #11 : Polynomials

Find the product:

**Possible Answers:**

**Correct answer:**

Find the product:

Step 1: Use the distributive property.

Step 2: Combine like terms.

### Example Question #11 : Polynomials

represents a positive quantity; represents a negative quantity.

Evaluate

**Possible Answers:**

The correct answer is not among the other choices.

**Correct answer:**

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 #12 : Polynomials

represents a positive quantity; represents a negative quantity.

Evaluate .

**Possible Answers:**

**Correct answer:**

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 #11 : Polynomials

and represent positive quantities.

Evaluate .

**Possible Answers:**

**Correct answer:**

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 #11 : Polynomials

Simplify the following expression:

**Possible Answers:**

**Correct answer:**

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:

### Example Question #31 : Variables

Define an operation on the set of real numbers as follows:

For all real ,

How else could this operation be defined?

**Possible Answers:**

**Correct answer:**

, as the cube of a binomial, can be rewritten using the following pattern:

Applying the rules of exponents to simplify this:

Therefore, the correct choice is that, alternatively stated,

.

### Example Question #21 : Polynomials

Solve for .

**Possible Answers:**

**Correct answer:**

Factor the expression

numerator: find two numbers that add to 2 and multiply to -8 [use 4,-2]

denominator: find two numbers that add to 5 and multiply to -14 [use 7,-2]

new expression:

Cancel the and cross multiply.

### Example Question #1 : Binomials

If 〖(x+y)〗^{2 }= 144 and 〖(x-y)〗^{2 }= 64, what is the value of xy?

**Possible Answers:**

16

20

22

18

**Correct answer:**

20

We first expand each binomial to get x^{2} + 2xy + y^{2} = 144 and x^{2} - 2xy + y^{2} = 64. We then subtract the second equation from the first to find 4xy = 80. Finally, we divide each side by 4 to find xy = 20.

### Example Question #382 : Algebra

Solve each problem and decide which is the best of the choices given.

What are the zeros of the following trinomial?

**Possible Answers:**

**Correct answer:**

First factor out a . Then the factors of the remaining polynomial,

, are and .

Set everything equal to zero and you get , , and because you cant forget to set equal to zero.

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