FACTORING BY GROUPING What is Factoring by Grouping
FACTORING BY GROUPING
What is Factoring by Grouping? Polynomials with more than three terms can be factored by a method called Factoring by Grouping, and sometimes different groupings will work. The purpose of this lesson is to factor polynomials by grouping.
FOR EXAMPLES: 1. Factor a³ - 2 a² - 3 a + 6 Solution: First, we write a³ and -2 a² in one quantity and -3 a and 6 in another quantity. Hence, we can now rewrite the given problem as (a³ - 2 a²) + (-3 a + 6)
Next, we take out the common monomial factor in each quantity. (a³-2 a²) = a²(a-2) = (a³ - 2 a²)
nd 2 Quantity (-3 a + 6) = -3 (a-2) = (-3 a + 6)
Notice that the terms inside the parenthesis are common to the two terms, so taking out again the common factor, we have (a-2) (a²-3)
OR: a³ - 2 a² - 3 a + 6 can be factored as (a³-3 a) + (-2 a² + 6) a (a²-3) + (-2)(a²-3) (a-2)
2. Factor 5 a³ - 10 a² + 3 a – 6 Solution: 5 a³ - 10 a² + 3 a – 6 = (5 a³ - 10 a²) + (3 a – 6) = 5 a² (a-2) + 3 (a-2) = (a-2) (5 a²+3)
3. Factor a² + 2 ab + b² - d² Solution: It is obvious that the first three terms are to be grouped together, since they form a perfect square trinomial, then, we have (a² + 2 ab + b²) - d²
Factoring the quantity (a² + 2 ab + b²) = (a+b) and rewriting the expression, we have [(a+b)-d²] = (a+b)² - d² notice that the expression is classified as the difference of two squares, and by the method of factoring.
we get, (a+b)²-d² = [(a+b)+d][(a+b)-d] = (a+b+d) (a+b-d) hence, a²+2 ab+b²-d² = (a+b+d)(a+b-d)
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