MPM2D: Chapter 5 Review 5.1 Multiply polynomials Distributive property FOIL: First, Outside, Inside, Last: (a + b)(c + d) = ac + ad + bc + bd 5.2 Special products Perfect squares: (a + b)2 = a2 + 2ab + b2 Difference of squares: (a + b)(a – b) = a2 – b2 5.3 Common factors Not all polynomials can be factored Greatest common factor (GCF): This can be factored out of each term of a polynomial. To find it, list each term’s prime factors, and find which prime factors are shared between all terms. The GCF is the product of the shared factors. Binomial common factor: When a binomial can be factored out of both terms, i.e.: 3x(y + 1) + 7z(y + 1) = (y + 1)(3x + 7z) Factor by grouping: Group the first two terms and the second two terms; pull out a common factor from both pairs of terms. If you can factor by grouping, both pairs will have the same common factor, and you can finish it like a binomial common factor. 5.4 Factor quadratic expressions of the form x2 + bx + c x2 + bx + c: Can often be factored to (x + r)(x + s), where b = r + s and c = rs. To factor, you want to find two values (r and s) that add to b and multiply to c. To help, you can list all of the factors of c, and find a pair that adds to b. Don’t forget negative factors! 5.5 Factor quadratic expressions of the form ax2 + bx + c ax2 + bx + c: Can often be factored to (ax + r)(x + s). To factor, you want to break up b into two pieces that add to b and multiply to ac. To help, you can list all of the factors of ac, and find a pair that adds to b. Once you have broken up b, you can write the result as ax2 + rx + sx + c. Then you can factor by grouping to get the final answer Don’t forget negative factors! 5.6 Factor a perfect square trinomial and a difference of squares Perfect square: a2 + 2ab + b2 = (a + b)2 Difference of squares: a2 – b2 = (a + b)(a – b) To recognize: Look for two square terms. If one square term is negative, it’s a difference of squares. If both are positive and there’s a middle term of 2ab, it’s a perfect square.