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Example 4-1a Factor In this trinomial,and You need to find two numbers whose sum is 27 and whose product is or 50. Make an organized list of factors of 50 and look for the pair of factors whose sum is 27. Factors of 50 Sum of Factors 1, 50 2, The correct factors are 2 and 25.

Example 4-1a Write the pattern. Group terms with common factors. Factor the GCF from each grouping. and Answer: Distributive Property Check You can check this result by multiplying the two factors. FOIL method FOIL Simplify.

Example 4-1a Factor Answer:

The correct factors are –4, –18. Example 4-1b Factor In this trinomial,and Since b is negative, is negative. Since c is positive, mn is positive. So m and n must both be negative. Therefore, make a list of the negative factors of or 72, and look for the pair of factors whose sum is –22. –73 –38 –27 –22 –1, –72 –2, –36 –4, –24 –4, –18 Sum of Factors Factors of 72

Example 4-1b Write the pattern. and Group terms with common factors. Factor the GCF from each grouping. Distributive Property Answer:

Example 4-1b a. Factor b. Factor Answer:

Example 4-2a , 82, 41, 82, 41, 82, 41, 82, 4 Sum of Factors Factors of 8 Factor Notice that the GCF of the terms, and 32 is 4. When the GCF of the terms of a trinomial is an integer other than 1, you should first factor out this GCF. Distributive Property Now factorSince the lead coefficient is 1, find the two factors of 8 whose sum is 6. The correct factors are 2 and 4.

Example 4-2a Answer: So,Thus, the complete factorization ofis

Example 4-2b Factor Answer:

Example 4-3a 14 –14 2 –2 –1, 15 1, –15 –3, 5 3, –5 Sum of Factors Factors of –15 Factor In this trinomial,and Since b is positive, is positive. Since c is negative, mn is negative, so either m or n is negative, but not both. Therefore, make a list of all the factors of 3(–5) or –15, where one factor in each pair is negative. Look for the pair of factors whose sum is 7.

Example 4-3a There are no factors whose sum is 7. Therefore, cannot be factored using integers. Answer:is a prime polynomial.

Example 4-3b Factor Answer: prime

Example 4-4a Solve Original equation Rewrite so one side equals 0. Factor the left side. orZero Product Property Solve each equation. Answer: The solution set is

Example 4-4b Solve Answer:

Example 4-5a Model Rockets Ms. Nguyen’s science class built an air-launched model rocket for a competition. When they test-launched their rocket outside the classroom, the rocket landed in a nearby tree. If the launch pad was 2 feet above the ground, the initial velocity of the rocket was 64 feet per second, and the rocket landed 30 feet above the ground, how long was the rocket in flight? Use the equation

Example 4-5a Vertical motion model Subtract 30 from each side. Factor out –4. Divide each side by –4. Factor orZero Product Property Solve each equation.

Example 4-5a The solutions areandseconds. The first time represents how long it takes the rocket to reach a height of 30 feet on its way up. The second time represents how long it will take for the rocket to reach the height of 30 feet again on its way down. Thus the rocket will be in flight for 3.5 seconds before coming down again. Answer: 3.5 seconds

Example 4-5b When Mario jumps over a hurdle, his feet leave the ground traveling at an initial upward velocity of 12 feet per second. Find the time t in seconds it takes for Mario’s feet to reach the ground again. Use the equation Answer: second