FACTORS A Monomial can be written as a product of its factors. A Monomial can be written as a product of its factors. Example: Example: a 2a = 2 * a a 3a 2 b = 3 * a * a * b The common factor of 2a and 3a 2 b is a

Greatest Common Factor You can also find the greatest common factor of two or more polynomials. You can also find the greatest common factor of two or more polynomials. 6m 2 n = 2 * 3 * m * m * n 9mn = 3 * 3 * m *n The GCF of 6m 2 n and 9mn is 3mn

FACTORING If the terms of a polynomial have a common factor, the polynomial can be written as a product. If the terms of a polynomial have a common factor, the polynomial can be written as a product. This is called factoring This is called factoring

EXAMPLES 4t + 12 Factor: 4t + 12 GCF = 4 4t = 4 * t 12 = 4 * 3 Step 1 – Find the GCF Step 2 – Divide to find the other factor 4t = t + 3 Therefore 4t + 12 = 4(t + 3) Check by expanding 4(t + 3) 4(t) +4(3) = 4t + 12

EXAMPLES Factor: 15a 3 – 10a a GCF = 5a 15a 3 = 3 * 5 * a * a * a 10a 2 = 2 * 5 * a * a 25a = 5 * 5 * a Step 1 – Find the GCF Step 2 – Divide to find the other factor 15a 3 – 10a a 5a = 3a 2 – 2a + 5 Therefore 15a 3 – 10a a = 5a(3a 2 – 2a + 5) Check by expanding 5a(3a 2 – 2a + 5) 5a(3a 2 ) +5a(-2a)+5a(5)=15a 3 – 10a a

Examples Write the monomial as a product of its factors. Write the monomial as a product of its factors. 1) 11p 2 = 11 * p * p 1) 11p 2 = 11 * p * p 2) 4cde = 2 * 2 * c * d * e 2) 4cde = 2 * 2 * c * d * e 3) 12x 2 yz = 3 * 2 * 2 * x * x * y * z 3) 12x 2 yz = 3 * 2 * 2 * x * x * y * z To multiply

You Try: Find the missing factor: Find the missing factor: A) 3w 2 = (__)(w) A) 3w 2 = (__)(w) B) 10pq = (___)(5p) B) 10pq = (___)(5p) C) (4b 2 )(___) = 12b 3 C) (4b 2 )(___) = 12b 3 D) 8m 2 n = (8mn)(__) D) 8m 2 n = (8mn)(__) E) -4xy = (___)(-y) E) -4xy = (___)(-y) F) (__)(-5j) = 20j 2 F) (__)(-5j) = 20j 2 Remember that you can divide to find the missing factor.

Solutions: Find the missing factor: Find the missing factor: A) 3w 2 = (3w)(w) A) 3w 2 = (3w)(w) B) 10pq = (2q)(5p) B) 10pq = (2q)(5p) C) (4b 2 )(3b) = 12b 3 C) (4b 2 )(3b) = 12b 3 D) 8m 2 n = (8mn)(m) D) 8m 2 n = (8mn)(m) E) -4xy = (4x)(-y) E) -4xy = (4x)(-y) F) (-4j)(-5j) = 20j 2 F) (-4j)(-5j) = 20j 2 Remember that you can divide to find the missing factor.

You Try Find the GCF of the two monomials Find the GCF of the two monomials A) 2pq, 2qr A) 2pq, 2qr B) 7a, 13ab B) 7a, 13ab C) 5xy, 15x 2 C) 5xy, 15x 2 D) 12s 2 t, 16st 2 D) 12s 2 t, 16st 2

Solutions Find the GCF of the two monomials Find the GCF of the two monomials A) 2pq, 2qrGCF = 2q A) 2pq, 2qrGCF = 2q B) 7a, 13abGCF = a B) 7a, 13abGCF = a C) 5xy, 15x 2 GCF = 5x C) 5xy, 15x 2 GCF = 5x D) 12s 2 t, 16st 2 GCF = 4st D) 12s 2 t, 16st 2 GCF = 4st 12s 2 t = 3 * 4 * s * s * t 16st 2 = 4 * 4 * s * t * t

You Try: Find the missing Factor: Find the missing Factor: A) 6m + 6n = (__)(m + n) A) 6m + 6n = (__)(m + n) B) 5h + 10 = (__)(h + 2) B) 5h + 10 = (__)(h + 2) C) 18y + 3y 2 = (__)(6 + y) C) 18y + 3y 2 = (__)(6 + y) D) 4x x = (__)(x + 3) D) 4x x = (__)(x + 3) E) -2a + 4 = (__)(a – 2) E) -2a + 4 = (__)(a – 2) F) -7cd 2 + 9d 2 = (__)(-7c + 9) F) -7cd 2 + 9d 2 = (__)(-7c + 9) Look for the GCF

Solutions Find the missing Factor: Find the missing Factor: A) 6m + 6n = (6)(m + n) A) 6m + 6n = (6)(m + n) B) 5h + 10 = (5)(h + 2) B) 5h + 10 = (5)(h + 2) C) 18y + 3y 2 = (3y)(6 + y) C) 18y + 3y 2 = (3y)(6 + y) D) 4x x = (4x)(x + 3) D) 4x x = (4x)(x + 3) E) -2a + 4 = (-2)(a – 2) E) -2a + 4 = (-2)(a – 2) F) -7cd 2 + 9d 2 = (d 2 )(-7c + 9) F) -7cd 2 + 9d 2 = (d 2 )(-7c + 9) Look for the GCF

Class work Lesson 26 Worksheet Lesson 26 Worksheet