Copy each problem. Then factor. 1.) x2 + 12x + 35 2.) x2 – 4x – 45 3.) x2 – 13x + 42 4.) x2 + 3x – 18 5.) x2 – 9x + 18 6.) x2 – 10x + 21

GCF, Trinomials where a ≠ 1 Factoring GCF, Trinomials where a ≠ 1

Factoring out the Greatest Common Factor The Greatest Common Factor (GCF) is the product of all the common factors. Decide what the biggest number is that is a factor of all the numeric parts of the terms, and then choose the smallest exponent on the variable (The GREATEST factor is the largest that you can “pull out.” You cannot pull or divide out 3 x’s if there are only 2.)

Example:

Try: Find the GCF of each.

Try: Find the GCF of each.

To factor out the GCF, write the GCF at the front and then divide each term by the GCF (this is the reverse of the distributive property!)

Factor out the GCF of each.

Factor out the GCF of each.

Factoring Trinomials of the Type For the equation , we would factor as follows: 1.) Enter the first and last terms into the upper left and lower right corners of the box as shown.

2.) Multiply the two numbers. The result will act like your old c. 2·2 = 4 3.) Find the factors of 4 that add up to 5, which the coefficient on the middle term, or b. 2·2 = 4 1·4 = 4 2 + 2 ≠ 5 1 + 4 = 5

4. ) Now, fill in the rest of the boxes as shown 4.) Now, fill in the rest of the boxes as shown. (It does not matter which number goes in which remaining box.) 5.) Find the GCF of each column and row. From the GCF of each column and row, the binomial factors are: (x + 2) (2x + 1)

Note: A GCF is negative if both terms are negative. The signs inside the binomial factors depend on the original trinomial (if a·c is positive, both signs are the same as b, and if a·c is negative, you must factor out the negative from the box).

Bottoms Up! As always, factor out the GCF. Multiply a·c and rewrite as x2 + bx + a·c Factor as before (what multiplies to give you a·c that adds or subtracts to give you b?) Divide the last term in each binomial by a. Simplify the fractions. If there is still a fraction, move the denominator to the front of that binomial (Bottoms Up!) Check your answer using FOIL.