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Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Factoring Trinomials Section 5.3

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Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Factor a Trinomial Factor 2x 2 + 7x + 3: Using Algebra Tiles x 2 tile x tile unit tile

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Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Factor a Trinomial Using Algebra Tiles Place x tiles to form a rectangle. This rectangle represents 2x 2 + 7x + 3. 2x 2 + 7x + 3

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Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Factor a Trinomial Place 2 x tiles and one unit tile in the top row. Using Algebra Tiles Place one x tile and 3 unit tiles in the side column. The factors are (2x + 1) and (x + 3). 2x 2 + 7x + 3 = (2x + 1)(x + 3)

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Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Apply Factoring 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 – 3x 2, where d is the distance she can swim, and x is the speed in m/min. Scuba Diving A scuba diver uses up her air supply in 60 min when swimming at a speed of 30 m/min.

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Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Apply Factoring Express the distance formula in factored form. Scuba Diving Start by looking for a common factor A common factor is –3 Factor out –3 d = 1800 – 30x – 3x 2 d = –3(x 2 + 10x – 600)

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Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. Apply Factoring Scuba Diving Find two integers whose product is –600 and sum is 10. d = –3(x 2 + 10x – 600) The integers are 30 and –20 Factor 1Factor 2ProductSum d = --3(x + 30)(x –20) Factor 1Factor 2ProductSum 60--10--60050 Factor 1Factor 2ProductSum 60--10--60050 --12--60038 Factor 1Factor 2ProductSum 60--10--60050 --12--60038 40--15--60025 Factor 1Factor 2ProductSum 60--10--60050 --12--60038 40--15--60025 30--20--60010

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Copyright © 2010 McGraw-Hill Ryerson Limited, a Subsidiary of The McGraw-Hill Companies. All rights reserved. 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.

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