# GED Math : Quadratic Equations

## Example Questions

### Example Question #61 : Quadratic Equations

On which of the following would one use the FOIL technique?

Explanation:

The FOIL technique is used to multiply or expand two binomials. None of the other expressions represent two binomials. The closest representation would be . This expression calls for the multiplication of a binomial and a monomial, so a more straightforward application of the distributive property would work in that case.

### Example Question #62 : Quadratic Equations

Expand

Explanation:

One can use the FOIL method.

F:

O:

I:

L:

Adding them up, we get the polynomial , in the customary form of a polynomial.

### Example Question #63 : Quadratic Equations

Evaluate

Explanation:

So FOIL works in this case

F:

O:

I:

L:

### Example Question #64 : Quadratic Equations

Expand

Explanation:

This a case to FOIL

F:

O:

I:

L:

### Example Question #65 : Quadratic Equations

Expand

Explanation:

Even though there is an  in one of the expressions, the expression is STILL a binomial, and should be treated as such. FOIL is used with the multiplication of two binomials, so FOIL works here.

F:

O:

I:

L:

### Example Question #66 : Quadratic Equations

Multiply .

Explanation:

The FOIL method works because there are two binomials.

F:

O:

I:

L:

Multiply

Explanation:

We can use FOIL:

F:  x

O:  x

I:  x

L:  x

### Example Question #68 : Quadratic Equations

What is the degree of the polynomial represented as the product of the following two binomials?

A polynomial of degree 6.

A polynomial of degree 5.

A polynomial of degree 3.

A line.

A polynomial of degree 2

A polynomial of degree 5.

Explanation:

When the binomials are expanded, we get . This is a polynomial of degree 5.

### Example Question #69 : Quadratic Equations

A rectangular prism-shaped box is given as having a width, , a height 5 more than the width, and a length 4 more than 2 times the width. Write a polynomial that represents the area of the box, using FOIL.

Explanation:

First, we need to establish the dimensions of the box. We have the width, . The length is 4 more than 2 times the width, so we have , and the height is 5 more than the width, so we have .

We need to find the area. The area of a rectangular prism is given as length times width times height. So, we can write

To set it up using FOIL, it can be arranged as .

Through FOIL, we get , or .

### Example Question #70 : Quadratic Equations

Expand , keeping FOIL in the work.