 # 5.3.1 - Factoring. With quadratics, we can both expand a binomial product like (x + 2)(x + 5), or similar, and go the other way around Factoring = taking.

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5.3.1 - Factoring

With quadratics, we can both expand a binomial product like (x + 2)(x + 5), or similar, and go the other way around Factoring = taking a quadratic (trinomial) and writing it in terms of its binomial products

Methods for factoring: GCF = greatest common factor; find the biggest factor the numbers have in common Tree = using a tree to come up of the factors of a particular number, then writing as the product

GCF When using the GCF, most common for when only factoring a binomial Consider the greatest factor for both the variable and the coefficients

Example. Factoring the expression 4x 2 + 8x Smallest power of variable? Largest number coefficients have in common?

Example. Factoring the expression 5y 3 – 15y 2 Smallest power of variable? Largest number coefficients have in common?

Factor the following three expressions using the GCF. 1) 10x 3 + 5x 2) 3x 2 – 9x 3 3) 15y 4 – 3y

“Tree” With trinomials, or quadratics with three terms, we can factor them into their respective binomial factors The trick will be to use factor trees, similar to those used in classes before

Using trees To use the three, consider the expression x 2 + 4x + 3 We need the factors of the constant that will add to the middle Factors of 3?

Example. Factor the expression x 2 + 6x + 8 Factors of constant? Which add to the middle?

Example. Factor the expression x 2 - 3x - 10 Factors of constant? Which add to the middle?

Example. Factor the expression x 2 + 2x - 15 Factors of constant? Which add to the middle?

Assignment PG. 237 15-31 odd

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