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Factors and Factoring

In this lesson, we explore the concept of factors and factoring in mathematics. A monomial can be expressed as a product of its factors, with example calculations for the greatest common factor (GCF) provided. Learn how to factor polynomials by identifying common factors, illustrated through various examples and practice problems. This lesson includes steps to find missing factors and to calculate GCFs for given monomials, enhancing your skills in algebraic manipulation and polynomial factorization.

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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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