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Factors and Factoring

Factors and Factoring. Lesson 26. FACTORS. A Monomial can be written as a product of its factors. Example:. The common factor of 2a and 3a 2 b is a. 2a = 2 * a 3a 2 b = 3 * a * a * b. Greatest Common Factor.

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Factors and Factoring

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  1. Factors and Factoring Lesson 26

  2. FACTORS • A Monomial can be written as a product of its factors. • Example: The common factor of 2a and 3a2b is a 2a = 2 * a 3a2b = 3 * a * a * b

  3. Greatest Common Factor • You can also find the greatest common factor of two or more polynomials. 6m2n = 2 * 3 * m * m * n 9mn = 3 * 3 * m *n The GCF of 6m2n and 9mn is 3mn

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

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

  6. EXAMPLES Factor: 15a3 – 10a2 + 25a Step 2 – Divide to find the other factor Step 1 – Find the GCF 15a3 – 10a2 + 25a 5a 15a3 = 3 * 5 * a * a * a 10a2 = 2 * 5 * a * a 25a = 5 * 5 * a = 3a2 – 2a + 5 GCF = 5a Therefore 15a3 – 10a2 + 25a= 5a(3a2 – 2a + 5) 5a(3a2 – 2a + 5) 5a(3a2) +5a(-2a)+5a(5)=15a3 – 10a2 + 25a Check by expanding

  7. Examples To multiply • Write the monomial as a product of its factors. • 1) 11p2 = 11 * p * p • 2) 4cde = 2 * 2 * c * d * e • 3) 12x2yz = 3 * 2 * 2 * x * x * y * z

  8. You Try: • Find the missing factor: • A) 3w2 = (__)(w) • B) 10pq = (___)(5p) • C) (4b2)(___) = 12b3 • D) 8m2n = (8mn)(__) • E) -4xy = (___)(-y) • F) (__)(-5j) = 20j2 Remember that you can divide to find the missing factor.

  9. Solutions: • Find the missing factor: • A) 3w2 = (3w)(w) • B) 10pq = (2q)(5p) • C) (4b2)(3b) = 12b3 • D) 8m2n = (8mn)(m) • E) -4xy = (4x)(-y) • F) (-4j)(-5j) = 20j2 Remember that you can divide to find the missing factor.

  10. You Try • Find the GCF of the two monomials • A) 2pq, 2qr • B) 7a, 13ab • C) 5xy, 15x2 • D) 12s2t, 16st2

  11. Solutions • Find the GCF of the two monomials • A) 2pq, 2qr GCF = 2q • B) 7a, 13ab GCF = a • C) 5xy, 15x2 GCF = 5x • D) 12s2t, 16st2 GCF = 4st 12s2t= 3 * 4 * s * s * t 16st2 = 4 * 4 * s * t * t

  12. You Try: • Find the missing Factor: • A) 6m + 6n = (__)(m + n) • B) 5h + 10 = (__)(h + 2) • C) 18y + 3y2 = (__)(6 + y) • D) 4x2 + 12x = (__)(x + 3) • E) -2a + 4 = (__)(a – 2) • F) -7cd2 + 9d2 = (__)(-7c + 9) Look for the GCF

  13. Solutions • Find the missing Factor: • A) 6m + 6n = (6)(m + n) • B) 5h + 10 = (5)(h + 2) • C) 18y + 3y2 = (3y)(6 + y) • D) 4x2 + 12x = (4x)(x + 3) • E) -2a + 4 = (-2)(a – 2) • F) -7cd2 + 9d2 = (d2)(-7c + 9) Look for the GCF

  14. Class work • Lesson 26 Worksheet

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