2 2 2 2 40 8 12 x y x y x 4 is a factor of all three terms 2 x is a factor of

2 2 2 2 40 8 12 x y x y x 4 is a factor of all three

This preview shows page 149 - 152 out of 433 pages.

2 2 2 2 40 8 12 x y x y x ± ± 4 is a factor of all three terms 2 x is a factor of all three terms. Divide each term by the 2 4 x . I think of what I need to multiply 2 4 x by to get each of the original terms of the 2 2 2 2 40 8 12 x y x y x ± ± You can check by multiplying. Factoring polynomials of the form x ² + bx +c factors of "c" whose sum is "b" write those numbers (x …)(x…) After we do an example we can see why it works by checking. ² ³ 2 5 3 5 2 3 ± ´ x x x ² ³ 3 4 5 2 3 10 25 15 2 5 3 5 x x x x x x ± ´ ± ´ ² ³ 10 2 3 4 2 2 ± ± y y x
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4.2 Factoring and Solving by Factoring page 150 By Will Tenney 3. Factor Steps Reasons b is 5 and c is 6 Look for the factors of "c" whose sum is "b". List factors of 6 1·6, -1·(-6), 2·3, -2·(-3) 2 and 3 have a sum of 5 Write those numbers after the (x …)(x …) When we check by multiplying, we see why the sum of the numbers is 5 and the product is 6. 4. Factor: Steps Reasons b is 5 and c is 24 List factors of -24 2·12 , 3·8, 3·( 8) 3 and 8 have a sum of 24 Look for the factors of "c" whose sum is "b". Write those numbers after the (x …)(x …) 5. Factor: 7 3 2 ´ ´ x x Steps Reasons 7 3 2 ´ ´ x x b is 3 and c is 7 List factors of 7 1·7, 1·( 7) Look for the factors of "c" whose sum is "b". None of the factors of 7 add up to 3 So, 7 3 2 ´ ´ x x does not factor. We can also say that 7 3 2 ´ ´ x x is prime. 6 5 2 ´ ´ x x 6 5 2 ´ ´ x x ² ³² ³ 3 2 ´ ´ x x ² ³² ³ 6 5 6 2 3 · 3 2 2 ´ ´ ´ ´ ´ ´ ´ x x x x x x x x 24 5 2 ± ± x x 24 5 2 ± ± x x ² ³² ³ 3 8 ´ ± x x In the FOIL we will always get x·x 2x + 3x = 5x We needed the sum to be 5 2·3 = 6 We only tried factors of 6
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4.2 Factoring and Solving by Factoring page 151 By Will Tenney 6. Factor: Steps Reasons First factor out the common factor. The factors of 3 whose sum is 2 are 3 and 1. Keep the common factor of 6x. Factoring polynomials of the form ax ² + bx + c by Guess and Check: We are doing FOIL backwards. ax ² is coming from the first terms and c is coming from the last terms. We can check all possibilities that will give us ax ² and c . Then we check the FOIL to see if we have the right bx term. Examples 7. Factor 2x ² + 7x + 3 Steps Reasons 2x ² must factor into 2x and x in the first two terms. Check: The factors of 3 are 1,3 and . Try them in both possible orders. They would not be negative because the middle term 7x is positive. If you check the FOIL the answer is the second choice. Check: Here we are guessing 2x and x for the first part of the factors because they will give us 2x ² in the FOIL. We guess 1 and 3 for the second part of the factors because they will give us 3 in the FOIL. We have to try the various combinations and do the FOIL to see which combination works.
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