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Factor. x² - 3x - 4 Factors into two binomials: -1st terms are factors of x²....x and x - 2nd terms multiply to get -4 and add to get -3.....+1 and - 4 x² - 3x – 4 = (x + 1)(x - 4) {factored into two binomials} © Algebra House Factor out the greatest common factor.
13x²yz + 169xy²z² - 39xyz² {when choosing GCF of same variables, choose smallest exponent} GCF of 13, 169, and 39.....is 13 GCF of x², x, and x........is x GCF of y, y² and y........is y GCF of z, z², and z³......is z GCF is 13xyz = 13xyz(x + 13yz - 3z²) {factored out the GCF by dividing each term by it} © Algebra House Simplify by factoring
5z - 40 -------- 8 - z 5(z - 8) --------- {factored 5 out of top and switched bottom around} -z + 8 5(z - 8) ---------- {factored -1 out of bottom} -1(z - 8) = - 5 {cancelled z - 8 on top and bottom} © Algebra House |
Factor. x² + 2x - 15 Factors into two binomials: -1st terms are factors of x²....x and x - 2nd terms multiply to get -15 and add to get 2....+5 and -3 x² + 2x – 15 = (x + 5)(x - 3) {factored into two binomials} © Algebra House Factor the difference of two cubes
8a³ - 64 It is a difference of two cubes in the form a³ - b³, it factors into the form (a - b)(a² + ab + b²) If a³ is 8a³, then a is 2a {the cube root of 8a³} If b³ is 64, then b is 4 {the cube root of 64} 8a³ - 64 = (2a - 4)(4a² + 8a + 16) {substituted 2a, in for a, and 4, in for b, into (a - b)(a² + ab + b²)} © Algebra House Factor by grouping
2ax - ay + 2bx – by = 2ax + 2bx - ay - by {re-arranged the terms, grouping terms with common factors together} = 2x(a + b) - y(a + b) {factored 2x out of 1st two terms and -y out of 3rd and 4th terms} = (a + b)(2x - y) {factored out the greatest common factor, a + b} © Algebra House |
