1. Factoring Algebraic Expressions Multiplying a Polynomial by a Monomial Multiplying a Binomial by a Binomial Dividing a Polynomial by a Monomial Dividing a Polynomial by a Binomial Factoring Polynomials Trinomials

2. Multiplying a Polynomial by a Monomial Rule 8 ‑ 1: When multiplying a polynomial by a monomial, there must be as many terms in the answer as there are in the polynomial. 3x(4x ‑ 2y + 4) = 12x 2 ‑ 6xy + 12x

3. Multiplying a Binomial by a Monomial Key Point: When multiplying a binomial by a binomial, multiply each term in the multiplicand by each term in the multiplier. (a+4)(a-2) a 2 +4a-2a-8 a 2 +2a-8

4. Dividing a Polynomial by a Binomial Key Point: When dividing a polynomial by a monomial, divide each term in the polynomial by the monomial. (6x 3 + 12x 2 ‑ 3x)  3x = 2x 2 + 4x ‑ 1

5. Dividing a polynomial by a binomial Key Point: When dividing a polynomial by a binomial, set it up as a long ‑ division problem with the literal numbers in descending order; then perform the division.

6. Factoring Polynomials Rule 8 ‑ 2: To factor a polynomial: 1. Find the prime factors of each term. 2. Determine the factors common to all terms. 3. Factor the polynomial by dividing the polynomial by the common factors. Factor: 6a 2 + 12a - 18a 3 6a 2 = 2 3 a 2 12a = 2 2 3 a 18a 3 = 2 3 3 a 3 The common factors are 2 3 a = 6a 6a 2 + 12a - 18a 3  6a = a + 2 - 3a 2 6a(a + 2 - 3a 2 ) =6a( -3a 2 + a + 2)

7. Trinomials Key Point: Trinomials can be factored if we can find two numbers whose sum is the coefficient of the second term and whose product is the third term. Factor x 2 + 13x + 42. (x + 7)(x + 6)