CCA 8.1.3 Factoring - Special Cases QUIZ - 15Q + 1 Silly!
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One of the keys to factoring is finding patterns between the trinomial and the factors of the trinomial. Learning to recognize a few common polynomial types will lessen the amount of time it takes to factor them. Knowing the characteristic patterns of special products—trinomials that come from squaring binomials, for example—provides a shortcut to finding their factors.
Perfect squares are numbers that are the result of a whole number multiplied by itself or squared. For example, 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 are all perfect squares—they come from squaring each of the numbers from 1 to 10. Notice that these perfect squares can also come from squaring the negative numbers from −1 to −10, like (−1)( −1) = 1, (−2)( −2) = 4, (−3)( −3) = 9, and so on.
A perfect square trinomial is a trinomial that is the result of a binomial multiplied by itself or squared. For example, (x + 3)2 = (x + 3)(x + 3) = x2 + 6x + 9. The trinomial x2 + 6x + 9 is a perfect square trinomial. In standard form, the first and last terms are always perfect squares. The middle term is the product squareroots of first and last terms multiplied by 2. The middle term can be positive or negative.
If the B-term is not present, we have a difference of squares situation.
A binomial in the form a2 – b2 can be factored as (a + b)(a – b).
Examples: The factored form of x2 – 100 is (x + 10)(x – 10).
The factored form of 49y2 – 25 is (7y + 5)(7y – 5).
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