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Factoring

How to Factor Trinomial with Leading Coefficient of One, Part Two

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Algebra
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Part Two
After determining the signs of the resulting binomials, we need to determine the numbers that belong in each binomial. Because the leading coefficient is one, the leading coefficient of each binomial will be one. This is how your factored trinomial will look like: (x+3)(x-2) . To determine the numbers, we must look again at the second sign between terms in the trinomial. If positive, we must find two factors of the last term that add up to the coefficient of the second term. These numbers will be the ones that go in the binomials. (See part one to determine which number goes in which binomial.) If the second sign is negative, then you must find two factors of the last term that subtract to the coefficient of the middle term.

How to Factor Trinomial with Leading Coefficient of One, Part One

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First, organize the polynomial in terms of order (2nd, 1st, and 0). Then, note the signs between each term of the polynomial. If the second sign is positive, then the signs between each term of each resulting binomial will be the same. You can determine this sign by looking at the first algebraic sign between terms. If the sign is positive, both signs will be positive. If the sign is negative, both signs will be negative. If the second sign is negative, both signs in the resulting binomials will be opposite. If the first sign is positive, then the sign next to the biggest constant in the binomial will be positive, and vice versa.

Factoring Polynomials of Degree 3

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Factoring Polynomials of Degree 3 Factoring a 3 - b 3 An expression of the form a 3 - b 3 is called a difference of cubes. The factored form of a 3 - b 3 is (a - b)(a 2 + ab + b 2) : (a - b)(a 2 + ab + b 2) = a 3 - a 2 b + a 2 b - ab 2 + ab 2 - b 3 = a 3 - b 3 For example, the factored form of 27x 3 - 8 ( a = 3x, b = 2 ) is (3x - 2)(9x 2 + 6x + 4) . Similarly, the factored form of 125x 3 -27y 3 ( a = 5x, b = 3y ) is (5x - 3y)(25x 2 +15xy + 9y 2) . To factor a difference of cubes, find a and b and plug them into (a - b)(a 2 + ab + b 2) . Factoring a 3 + b 3 An expression of the form a 3 + b 3 is called a sum of cubes. The factored form of a 3 + b 3 is (a + b)(a 2 - ab + b 2) : (a + b)(a 2 - ab + b 2) = a 3 + a 2 b - a 2 b - ab 2 + ab 2 + b 3 = a 3 - b 3 .
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