0. Write a paragraph describing in your own words what this unit is about?
In this unit you learn that you can factor using many different methods, about monomial, binomial, trinomial and polynomials. You learn how to solve them and how to factor them out. Throughout this lesson you will learn how to do all you need to do by using factoring.
1. What is monomial, trinomial, and a polynomial?
![Picture](/uploads/1/5/2/4/15247484/7368752.gif?554)
A monomial is an expression, a variable, or a product of a number and no more variables.
Example: 9
A binomial is a polynomial of two terms.
Example: 3x + 7
A polynomial is a sum of one or more monomials. A quotient with a variable in the denominator is not is not a polynomial.
Example: 2x^2
Example: 9
A binomial is a polynomial of two terms.
Example: 3x + 7
A polynomial is a sum of one or more monomials. A quotient with a variable in the denominator is not is not a polynomial.
Example: 2x^2
2. How do you find the degree of a polynomial?
How you find a degree of a polynomial is when one variable is the same as the degree of the monomial with the greatest exponent.
Naming a polynomial is a simple as the same as the following. When you see
something like this: 7x + 4
is called a first degree binomial... why? Because there is one exponent and so is the FIRST, meaning one and then there is two polynomials 7x and 4 is a
binomial. Another example is: 3x^2 + 2x + 1 is called a quadratic trinomial. In this one it's a quadratic which is because the exponent is two and that means is quadratic. There us three polynomials so it' a trinomial. The last last example Iwill give: 5. Simply called a monomial since it is a number.
Naming a polynomial is a simple as the same as the following. When you see
something like this: 7x + 4
is called a first degree binomial... why? Because there is one exponent and so is the FIRST, meaning one and then there is two polynomials 7x and 4 is a
binomial. Another example is: 3x^2 + 2x + 1 is called a quadratic trinomial. In this one it's a quadratic which is because the exponent is two and that means is quadratic. There us three polynomials so it' a trinomial. The last last example Iwill give: 5. Simply called a monomial since it is a number.
3.How do you multiply 2 polynomials using the distributive property?
![Picture](/uploads/1/5/2/4/15247484/7084516.gif)
4. How do you multiply 2 biomomials.
The way you multiply two binomials is either by
foiling or box method. Foiling is when you do the following: (x+5)
(x-3)
First: x * x = x^2
Outer: x
* -3= -3x
Inner: 5 *x = 5x
Last: 5 * -3:
-15
The add the like terms and put them together:
x^2 + 2x -
15
The other way which is called the box method. When you do the box method you do as followed:
x
5
x
x^2 5x
-3 -3x
-15
= x^2 + 2x - 15
As you see you get the same anwser with either one, I personally enjoy the box method but foiling works just as well.
foiling or box method. Foiling is when you do the following: (x+5)
(x-3)
First: x * x = x^2
Outer: x
* -3= -3x
Inner: 5 *x = 5x
Last: 5 * -3:
-15
The add the like terms and put them together:
x^2 + 2x -
15
The other way which is called the box method. When you do the box method you do as followed:
x
5
x
x^2 5x
-3 -3x
-15
= x^2 + 2x - 15
As you see you get the same anwser with either one, I personally enjoy the box method but foiling works just as well.
5. What does it mean to factor?
Factoring is breaking it down in (x+a) (x+b). Then
the solutions
are x+a and x+b so for
example:
x^2 + 5x
+4
Ask yourself,
what two numbers add to 5 and mutiply to 4.
(x+1) (x+4) is
how you
would write your anwser.
By
factoring a number, you do the
following:
2= 1 x 2
4= 2 x 2
the solutions
are x+a and x+b so for
example:
x^2 + 5x
+4
Ask yourself,
what two numbers add to 5 and mutiply to 4.
(x+1) (x+4) is
how you
would write your anwser.
By
factoring a number, you do the
following:
2= 1 x 2
4= 2 x 2
6. How do you factor a trinomial when a=1.
FORMULA: ax^2 + b + c= (x+y) (x+z)
You need to find
2 numbers, y and z that mulitply to equal a x c and that add to equal b.
x^2 + 13x + 36
a= 1
b=
13
c= 36
(x+4) (x+9)
You need to find
2 numbers, y and z that mulitply to equal a x c and that add to equal b.
x^2 + 13x + 36
a= 1
b=
13
c= 36
(x+4) (x+9)
7.What is a difference of sqaures.
![Picture](/uploads/1/5/2/4/15247484/6670116.jpg)
The difference of squares is that you have to make
sure that they are all the same. Like for an example:
(3^4
+ 8^3 +3^2) + (7^2 + 9^4 - 2^3)
How you solve this one is that you have to make sure all the
squares are in order, like the first one is 4,3,2 also known as biggest to
smallest, if there was a number you would have to put it last and then
solve.
sure that they are all the same. Like for an example:
(3^4
+ 8^3 +3^2) + (7^2 + 9^4 - 2^3)
How you solve this one is that you have to make sure all the
squares are in order, like the first one is 4,3,2 also known as biggest to
smallest, if there was a number you would have to put it last and then
solve.
8. What is the relationship beween multiplying and factoring?
The relationship of factoring a multiplying is
that when you factor
out a number, for example, 6, what times what = 6? 2 and
3. 2 times 3 = 6.
So when you are factoring you have to be able to be able to
multiply the
numbers and be able to get then number you are
factoring.
that when you factor
out a number, for example, 6, what times what = 6? 2 and
3. 2 times 3 = 6.
So when you are factoring you have to be able to be able to
multiply the
numbers and be able to get then number you are
factoring.