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Trinomials: Simple: ax^2+bx+ c, a=1 Complex: ax^2+bx+c, a≠1 Perfect: a^2+2ab+b^2= (a+b)^2 or a^2-2ab-b^2= (a-b)^2
Complex Trinomials
Decomposition: 1. Find two numbers that multiply to the product of a & c that also add to b. 2. Rewrite & replace term bx with the two numbers, split the equation in half. 3. Now factor out the GCF of each binomial. 4. The binomials should be the same, leaving the factored-out numbers to create a binomial & replace one of the brackets.
Trial and Error: 1. Check the equation is complex. 2. Find factor pairs for term 1 & 3. 3. Cross multiply the pairs & add the products. 4. The added product should be the same as bx, and if different, re-do with another pair. 5. If correct, use the correct pair to multiply & create two binomials. 6. Using each of the added numbers, create two binomials, one pair for each binomial.
Simple Trinomials: Sum and Product 1. Analyze the equation. 2. For the sum, find two numbers that add up to b. 3. For the product, find two numbers that multiply to c. 4. The two numbers added in the sum must be the same numbers used in the product. 5. Create two binomial brackets, an x in each, followed by the sum in one and the product in the other brackets.
Perfect square Trinomials: 1. Be sure 1st & 3rd terms are perfect squares. 2. Be sure the middle term is twice the product of the square roots of terms 1 & 3. 3. Write as a squared binomial. The sign separating the binomial should be the same as the middle term from the trinomial.
Difference of Squares ?
Factoring difference of squares: 1. Find the square root of each term. 2. Write the roots and separate by a minus, then bracket the expression. 3. Do it beside it again but with a plus instead.
No/Done
