Page 615 - Algebra 1

Some trinomials of the form ax2 + bx + c can also be factored. The following activity will demonstrate this factorization through the use of algebra tiles.
Exploration Factoring Trinomials of the Form ax2 + bx + c Using Algebra Tiles
Factor 2x2 + 7x + 3.
Collect two x2-tiles, seven x-tiles, and three 1-tiles.
28. Build a rectangle using the algebra tiles. Keep the x2-tiles on the top row of the rectangle. Fill in the x-tiles horizontally below and vertically to the right of the x2-tiles. Use the 1-tiles to fill in the gaps of the rectangle. Remember that the lines between the tiles must be completely vertical or horizontal across the entire pattern.
Observe that the top edge of the pattern represents the length of a rectangle. The side edge of the pattern represents the width of a rectangle.
29. Using the sides without the x2-tiles, how can the length and width of the rectangle be represented?
30. How is the area of a rectangle calculated?
31. Write an expression for the area of the rectangle using the length and
width previously found.
32. What is the factored form of 2x2 + 7x + 3?
To review factoring polynomials, first look for common factors of the terms. If there is a common factor, find the GCF, and then factor it out of the polynomial. After factoring out the GCF, look for patterns.
Pattern 1: If the polynomial has two terms, then look for the difference of two squares.
Pattern 2: If the polynomial has three terms, look for a perfect-square trinomial. If the trinomial is not a perfect square, try to factor using the method for general trinomials of the form x2 + bx + c orax2 +bx+c.
Pattern 3: If the polynomial has four terms, try to factor by grouping.
Examine the resulting polynomial factor(s) to determine if any can be factored further. If so, continue the process. If not, factoring is complete. Remember that the factored result can always be verified through multiplication and simplification.
600 Saxon Algebra 1