8.2 Factoring using the GCF & the Distributive Property Algebra 1 8.2 Factoring using the GCF & the Distributive Property Factor: 29xy – 3x Ask yourself: What is Common in both parts? 29xy & 3x The x is common so you factor it out. Which is like “backwards or reverse distribution”. x (29y – 3) Factor this one: 3y2 + 12 The 3 is common in both parts…therefore 3(y2 + 4)

More Factoring Factor: 11x + 44x2y 11x(1 + 4xy) Factor: 16a + 4b Factor: 3p2q – 9pq2 + 36pq 3pq(p – 3q + 12)

Factoring by Grouping Using the distributive property to factor polynomials having four or more terms. (3mx + 2my) + (3kx + 2ky) What’s common in the first 2? m What’s common in the second 2? k Therefore, m(3x + 2y) + k(3x + 2y) Take a look at the “big picture” – what’s the same? (3x + 2y) – therefore we can factor it out (3x + 2y)(m + k)

More factoring 2ax + 6xc + ba + 3bc 2x(a + 3c) + b(a + 3c) (a + 3c)(2x + b) 2ax + ab + 6cx + 3bc a(2x + b) + 3c(2x + b) (2x + b)(a + 3c)

Using the Additive Inverse Property Factor: c – 2cd + 8d – 4 c(1 - 2d) + 4(2d – 1) Notice that the parentheses are slightly different (just opposite signs) Therefore you need to factor out a -1 from one of the parentheses c (-1)(-1 + 2d) + 4(2d – 1) -c (2d – 1) + 4(2d – 1) (2d – 1)(-c + 4)

Solve equations in factored form using the Zero Product Property Set each parentheses equal to zero and solve. (d + 5)(d – 3) = 0 d + 5 = 0 d – 3 = 0 d = -5 d = 3 Solution Set {-5,3} (2x + 4)(3x – 6) = 0 2x + 4 = 0 3x – 6 = 0 2x = -4 3x = 6 x = -2 x = 2 Solution Set {-2,2} Roots: The solutions of an equation.

Add another step! y2 = 6y Rewrite so it = 0 y2 – 6y = 0 GCF y(y – 6) = 0 Set each = 0 y = 0 y – 6 = 0 Get y by itself (solve for y) y = 0 y = 6 Solution Set {0,6}

Homework #57 p. 429 10-28, 32, 38