2.07 Factoring out the greatest common factor (GCF)
Find the greatest common factor between each set of terms:
3 and 15 x
8 a and 9 a
33 x and 6 x^{2}
12 b and 15 b^{2} x
Complete the following statements:
4 r + 12 = ⬚ \left(r + 3\right)
5 v - 30 = ⬚ \left(v - 6\right)
18 c - 24 = ⬚ \left( 3 c - 4\right)
2 t^{2} + 2 t = 2 t \left(⬚ + ⬚\right)
Factor the following expressions:
6 v + 30
45 t - 40
- 2 s - 10
- 12 s + 10
y^{2} + 4 y
k^{2} - 5 k
2 u^{2} - 8 u
4 t + 2 t^{2}
42 x - x^{2}
7 x + 35
36 - 6 x
- 2 x + 10
- 100 - 10 x
- 18 y^{2} + 6
9 \left( 3 x + 4\right) + 4 \left( 3 x + 4\right)
8 t \left(t - 3\right) + 9 \left(t - 3\right)
Xander was asked to factor the expression 35x^2y+10xy^2-5xy. Identify his error.
Xander:
The greatest common factor is 5xy so the factored form of the expression is 5xy(7x+2y)
A farmer wants to create a set of adjacent fields which all have the same width. He plans to create the smallest field in the shape of a square, with the largest field 9 times the size of the smallest field, and the middle field to have a length that is 5 units more than the smallest field.
Write expressions for the area of each field.
Use factoring to determine the dimensions of the entire field.
Explain how dividing monomials relates to factoring the greatest common factor.
Explain why the greatest common factor of the variables in any expression has the least possible exponent of any of the terms.
You are to design a photo collage made of two large square photos with a side length of x and four smaller rectangular photos that have a height of x and a width of 4 inches.
Find an algebraic expression for the area of the rectangle formed if the photos are all placed in a single row. Draw an example of what this arrangement would look like.
Fully factor your answer from part (a) and then draw a photo arrangement that would match these dimensions.