Factoring Trinomials 1 Factor In this trinomial and

Factoring Trinomials 1

Factor In this trinomial, and You need to find the two numbers whose sum is 7 and whose product is 12. Make an organized list of the factors of 12, and look for the pair of factors whose sum is 7. Factors of 12 Sum of Factors 1, 12 2, 6 3, 4 Answer: 13 8 7 The correct factors are 3 and 4. Write the pattern. and

Check You can check the result by multiplying the two factors. F O I L FOIL method Simplify.

Factor Answer:

Factoring - Signs • If the last term is positive – Both new middle terms have the same sign, and the sign is the same as the old middle term • If the last term is negative – The new middle terms have different signs, and the larger term has the same sign as the old middle term

Factor In this trinomial, and This means is negative and mn is positive. So m and n must both be negative. Therefore, make a list of the negative factors of 27, and look for the pair whose sum is – 12. Factors of 27 Sum of Factors – 1, – 27 – 3, – 9 Answer: – 28 – 12 The correct factors are – 3 and – 9. Write the pattern. and

Check You can check this result by using a graphing calculator. Graph and on the same screen. Since only one graph appears, the two graphs must coincide. Therefore, the trinomial has been factored correctly.

Factor Answer:

Factor In this trinomial, and This means is positive and mn is negative, so either m or n is negative, but not both. Therefore, make a list of the factors of – 18 where one factor of each pair is negative. Look for the pair of factors whose sum is 3. Factors of – 18 1, – 18 – 1, 18 2, – 9 – 2, 9 3, – 6 – 3, 6 Sum of Factors – 17 17 – 7 7 The correct factors – 3 are – 3 and 6. 3

Write the pattern. Answer: and

Factor Answer:

Factor Since and is negative and mn is negative. So either m or n is negative, but not both. Factors of – 20 Sum of Factors 1, – 20 – 1, 20 2, – 10 – 2, 10 4, – 5 – 4, 5 – 19 19 – 8 8 – 1 1 The correct factors are 4 and – 5.

Answer: Write the pattern. and

Factor Answer:

Homework Quiz

Solve Check your solutions. Original equation Rewrite the equation so that one side equals 0. Factor. or Zero Product Property Solve each equation. Answer: The solution is

Check Substitute – 5 and 3 for x in the original equation.

Solve Answer: Check your solutions.

Architecture Marion has a small art studio measuring 10 feet by 12 feet in her backyard. She wants to build a new studio that has three times the area of the old studio by increasing the length and width by the same amount. What will be the dimensions of the new studio? Explore Begin by making a diagram like the one shown to the right, labeling the appropriate dimensions.

Plan Let the amount added to each dimension of the studio. The new length times the new width equals the new area. old area Solve Write the equation. Multiply. Subtract 360 from each side.

Factor. or Zero Product Property Solve each equation. Examine The solution set is Only 8 is a valid solution, since dimensions cannot be negative. Answer: The length of the new studio should be or 20 feet and the new width should be or 18 feet.

Photography Adina has a photograph. She wants to enlarge the photograph by increasing the length and width by the same amount. What dimensions of the enlarged photograph will be twice the area of the original photograph? Answer:

Homework • 9 -3 Two Pages, Evens