Factoring Trinomials Section 5.3

Factor a Trinomial Using Algebra Tiles Factor 2x2 + 7x + 3: x2 tile unit tile

Factor a Trinomial Using Algebra Tiles 2x2 + 7x + 3 Place x tiles to form a rectangle. This rectangle represents 2x2 + 7x + 3.

The factors are (2x + 1) and (x + 3). Factor a Trinomial Using Algebra Tiles Place 2 x tiles and one unit tile in the top row. Place one x tile and 3 unit tiles in the side column. The factors are (2x + 1) and (x + 3). 2x2 + 7x + 3 = (2x + 1)(x + 3)

Apply Factoring Scuba Diving A scuba diver uses up her air supply in 60 min when swimming at a speed of 30 m/min. If she swims faster, she will cover more distance each minute, but will also breathe more quickly, depleting her air supply more quickly. If she swims at 30 + x m/min, the distance she can swim before running out of air is given by the formula d = 1800 – 30x – 3x2, where d is the distance she can swim, and x is the speed in m/min.

Express the distance formula in factored form. Apply Factoring Scuba Diving Express the distance formula in factored form. d = 1800 – 30x – 3x2 Start by looking for a common factor A common factor is –3 Factor out –3 d = –3(x2 + 10x – 600)

Apply Factoring Scuba Diving d = –3(x2 + 10x – 600) Find two integers whose product is –600 and sum is 10. Factor 1 Factor 2 Product Sum 60 --10 --600 50 Factor 1 Factor 2 Product Sum 60 --10 --600 50 --12 38 Factor 1 Factor 2 Product Sum 60 --10 --600 50 --12 38 40 --15 25 30 --20 10 Factor 1 Factor 2 Product Sum 60 --10 --600 50 --12 38 40 --15 25 Factor 1 Factor 2 Product Sum The integers are 30 and –20 d = --3(x + 30)(x –20)

Apply Factoring Scuba Diving Did You Know? A scuba diver can make maximum use of the available air by breathing slowly and deeply. Slow, deep breathing allows the lungs to transfer more oxygen from the air to the blood before it is exhaled. Once the air is exhaled, it disappears as bubbles.