Factoring Quadratics PDF
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This document provides examples of factoring quadratic expressions of the form x² + bx + c where b and c are positive or negative. The examples include working through the factors, the sum of factors and showing step-by-step how to complete the expression. A word problem on the area of a rectangle is also included.
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Factoring x² + bx + c, when b and c are POSITIVE Ex: Factor x² + 10x + 16 b = 10 and c = 16 Since c is POSITIVE, the factors p and q must have the SAME sign so that pq is POSITIVE Since b is POSITIVE, p and q must EACH be POSITIVE so that p + q is...
Factoring x² + bx + c, when b and c are POSITIVE Ex: Factor x² + 10x + 16 b = 10 and c = 16 Since c is POSITIVE, the factors p and q must have the SAME sign so that pq is POSITIVE Since b is POSITIVE, p and q must EACH be POSITIVE so that p + q is POSITIVE c b x² + 10x + 16 = (x + 2)(x + 8) Factoring x² + bx + c, when c is NEGATIVE, p and q have DIFFERENT signs Ex: Factor x² + 4x - 21 b = 4 and c = - 21 Since c is NEGATIVE, the factors p and q must have DIFFERENT signs so that pq is NEGATIVE c b x² + 4x - 21 = (x - 3)(x + 7) Ex: A farmer plants a rectangular pumpkin patch in the northeast corner of the square plot of land. The area of the pumpkin patch is 600 square meters. What is the area of the square plot of land? The length of the patch is (s – 30) meters and the width is (s – 40) meters. Write and solve an equation for its area. Since the diagram shows the land’s side length is AT LEAST 30 meters, the factor of 10 meters does not make sense. Therefore, the width of the square plot of land is 60 meters and the area is A = bh = (60)(60) = 3600 square meters.
