The area of a rectangular knitted blanket is #9x^2 - 6x - 8#. What are the possible dimensions of the blanket?

1 Answer
Jim G.
Aug 18, 2017

#3x-4" and "3x+2#

Explanation:

#"since area of rectangle "="length "xx" width"#

#"we are looking for the factors of "9x^2-6x-8#

#"here "a=9,b=-6,c=-8#

#"consider the factors of ac which sum to b"#

#"that is product of "9xx-8=-72 " with sum "=-6#

#"the 2 factors then are - 12 and + 6"#

#rArr9x^2-6x-8#

#=9x^2-12x+6x-8larr -12x+6x=-6x#

#"factorise by grouping"#

#=color(red)(3x)(3x-4)color(red)(+2)(3x-4)#

#"factor out "(3x-4)#

#=(3x-4)(color(red)(3x+2))#

#rArr9x^2-6x-8=(3x-4)(3x+2)#

#"the possible dimensions are "3x-4" and "3x+2#

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