4.6 Reasoning About Factoring Polynomials
You can use the following checklist to decide how to factor an algebraic expression:
Divide out all the common factors first.
If the expression has two terms, check for a difference of squares: a － b = (a + b)(a － b)
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If the expression has three terms and is in the form x2 + bx + c, then factor the sum and product.
ie: m + n = b and (m)(n) = c If the expression has three terms and is in the form ax2 + bx + c, then factor criss­cross method.
If the expression has four or more terms, factor by grouping. 1
Factoring Strategies
Factoring is the process where a polynomial expression is written as a product of other algebraic expressions.
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Practice: Factor completely
a) x2 ­ 6x ­ 27 c) ­18x4 + 32x2
b) x3 + 5x2 ­ 14x d) 16x2 ­ 88x + 121 e) x5y + x2y3 ­ x3y3 ­ y5 f) (x ­ 1)2 ­ (y + 7)2 3
A solid has volume defined by V = 4x3 ­12x2y + 9xy2.
Identify the type of solid.
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Determine a possible set of dimensions for each.
a)
b)
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Homework:
pg. 236 #6 ­ 13 and Workbook pages 6
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