3.3 ______
Some background information………
- Match each name in the left column with the correct examplein the right column.
Monomial
Binomial
Trinomial
Polynomial / 4x
x2 – 6x + 8
5x7 + 2xy – q3 – 99
10y + 8
- Given the following rectangles and their areas suggest what the sides might be. (Hint: the area of a rectangle is found by multiplying the sides,so the sides suggested must multiply to equal the area).
a) b) c) d)
e)
- Since the sides of the rectangles multiply to equal the area, the sides are ______of the area.
- Factor each of the following. Although there are many possible solutions for each, onlyone is needed. Ex. 12 = 2 x 6
a) 16 = b) 42 = c) 12x = e) 36c3 = g) 40x 6 =
- “to factor “something means to …
- Suggest a common factor for each pair or group. Only one answeris needed for each.
a) 9, 24 b) 30, 48, 60 c) 12 x 3, 18 x 4 d) 10 xy 4, 25 xy 5 e) 16 g3 k5, 72 g 4 k 7
7. Give the greatest common factor for each pair or group in # 6.
______Factoring
As seen in # 2, factoring can be modeled by determining the sides of a rectangle with a given area. Since the sides of a rectangle must multiply to equal the area, the sides are the factors of the area. Factoring polynomials can be modeled in the same manner using algebra tiles.
Model the following by drawing rectangles with the given area.
Identify and Label the sides to determine the factors.
Factor the polynomial.
a) 2x + 4 b) 4x + 6 c) 6x + 3 d) 3x – 6 e) x2 + 3x f) 2 x2 + 6x
g) 3 x2 + 3x h) 8x + 6 i) 4 x2 + 2x j)6x + 9 k) 6 x2 + 4x l) 4x + 2
m) 6 x2 + 3x n) 8x + 4
Conclusions
Have you noticed anything about your answers above that would allow you to factor without tiles? Hint: What do you notice about the monomial factor and how it relates to the terms in the polynomial being factored?
Use the above conclusion to try factoring the following without tiles.
a)6x + 4 b) 6x2 + 3x
How to Common Factor a Polynomial (without drawing)
To common factor:
1)Find the greatest common factor of the terms in the polynomial being factored. That will be one factor. Place it outside brackets.
Ex. 24x6y + 30x8y
The g.c.f. of the terms in the polynomial would be 6x6y so……
6x6y ( ? + ? )
2)Find the other factor, knowing it must multiply by the common factor (gcf) to equal the polynomial being factored. That will be the other factor. Place it inside the brackets.
Ex 24x6y + 30x8y
= 6x6y ( ? + ? )
= 6x6y ( 4 + 5x2 )
gcf multiplies by the common factor (gcf) to equal the polynomial being factored
How to Common Factor a Polynomial (without drawing)
To common factor:
1)Find the greatest common factor of the terms in the polynomial being factored. That will be one factor. Place it outside brackets.
Ex. 24x6y + 30x8y
The g.c.f. of the terms in the polynomial would be 6x6y so……
6x6y ( ? + ? )
2)Find the other factor, knowing it must multiply by the common factor (gcf) to equal the polynomial being factored. That will be the other factor. Place it inside the brackets.
Ex 24x6y + 30x8y
= 6x6y ( ? + ? )
= 6x6y ( 4 + 5x2 )
gcf multiplies by the common factor (gcf) to equal the polynomial being factored