By: William & Loc Multiply a polynomial by a monomial. Factor a monomial out of a polynomial. Finding Greatest Common Factors. A(b + c) = ab + ac -4y²(5y - 3y) Use the Distributive Property -20y³ + 12y³ Add coefficients and exponents with the + same base- Example: -4y²(5y³)= 20y² ³ Solve 1) 3m(m + 6) 2) 5b²(b + 4) 1) 3m² + 18m 2) 5b³ + 20b² 1) 4b(5b² + b + 6) 2) -7h(3h² - 8h – 1) 1)20b³ + 4b² + 24b 2)-21h³ + 56h²+ 7h GCF stands for 3 words: ◦ Greatest, ◦ Common and, ◦ Factor. Factors are the numbers you multiply together to get another number: 2x3=6 2 = factor 3 = factor ◦ Sometimes we want to find ALL the factors of a number: The factors of 12 are 1, 2, 3, 4, 6 and 12 ... ... because 2 × 6 = 12, or 4 × 3 = 12, or 1 × 12 = 12. Let say you have worked out the factors of two or more numbers: Example: _The factors of 12 are 1, 2, 3, 4, 6 and 12 _The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30. Then the common factors are those that are found in both lists (1,2,3 and 6). What are the common factors of 15, 30 and 105? The factors of 15 are 1, 3, 5, and 15 The factors of 30 are 1, 2, 3, 5, 6, 10, 15 and 30 The factors of 105 are 1, 3, 5, 7, 15, 21, 35 and 105. => The common factors are 1, 3, 5 and 15. <= It is simply the largest of the common factors. The GFC is the largest of the common factors of 2 or more numbers Find the GCF of 36 and 54: ◦ The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, and 36. ◦ The factors of 54 are 1, 2, 3, 6, 9, 18, 27, and 54. The common factors of 36 and 54 are: 1, 2, 3, 6, 9, 18. => GCF of 36 and 54 is 18. One of the most useful thing is when we want to simplify a fraction: ◦ Example: How can we simplify 12/30? ◦ Common Factors of 12 and 30 were 1, 2, 3 and 6, ◦ The Greatest Common Factor is 6. ◦ The largest number we can divide both 12 and 30 evenly by is 6: 12/30 = 2/5 (12 : 6 and 30 : 6) Two numbers 6 & 18 All factors 6: 1,2,3,4,6 18: 1,2,3,6,9,18 Common factors GCF Simplify fraction 1, 2, 3, 6 6 6/18 = 1/3 Find the GCF of the terms of 4x³ + 12x² - 8x List the prime factors of each term. Identify the factors common to all terms: ◦ 4x³ = 2 . 2 . x . x . x ◦ 12x² = 2 . 2 . 3 . x . x ◦ 8x = 2 . 2 . 2 . x => The GCF is 2 . 2 . x or 4x <= Two numbers 24 & 108 All factors 2 × 2 × 2 × 3 = 24, and 2 × 2 × 3 × 3 × 3 = 108 GCF Simplify fraction 2 × 2 × 3 = 12 6/18 = 1/3 Now let’s factor a monomial from a polynomial Factor 3x³ - 12x² First, find the GCF 3x³ = 3 · x · x · x 12x² = 2 · 2 · 3 · x · x Here, the GCF is 3x Lastly, factor out the monomial => 3x(x²) + 3x(-4x) <= Factor 3x from each term =>3x(x² - 4x) <= Final answer Use the GCF to factor the polynomials below. 8x² - 12x 5d³ + 10d 1) 4x(2x – 3) 2) 5d(d² + 2) Tutorial: You guys are to be divided into 4 teams. A set of questions will appear on the board. The team to answer all the questions on the board first will win points according to the slide.(Try to fit all answers on your board, and in the order) The team to score the most points at the end of the game wins! (You guys keep score) On the Board On your team’s board 1) problem 1) answer 2) problem 2) answer 3) problem 3) answer 1) (x + 8)2x 2) (3y + 5)6y 3) 9m(m + 6) 4) Find the GCF of the terms of 15w + 21w 1) 9m(2m + m + 4) 2) Find the GCF of the terms of: 5t² - 10 3) Factor out: 6x5 + 31x8 4) Factor out: y3 + 6y 1) -5x(8x² – 7 + 3x³) 2) 2n(4n + 5n + 8) 3) -10k(9k – 3k² - 6) 4) Factor out: 5p4 – 5p 1) Factor out: 8x2 + 2x – 18 2) 12c(-5c² + 3c – 4) 3) 3k(-7k - 2k + 5k³) Factor out #’s 1-3 1) 7x2 + 21x + 56 2) 19y7 + 5y7 3) 6x5 + 31x8 4) (4a² – 7a – 8)2a 2 + 2= ? Thanks for listening!