The area of a rectangular barnyard is given by the trinomial #4x^2+ 8x-21#. What are the possible dimensions of the barnyard?

1 Answer
Jim G.
Jun 7, 2017

#(2x-3)" and " (2x+7)#

Explanation:

#"the area of a rectangle "="length " xx" breadth"#

#"find the product of the factors of " 4x^2+8x-21#

#"factorise by 'splitting' the x term of the trinomial"#

#rArr4x^2+8x-21#

#=4x^2-6x+14x-21larr-6x+14x=8x#

#"take out a "color(blue)"common factor"" from each 'pair'"#
#"of terms"#

#=color(red)(2x)(2x-3)color(red)(+7)(2x-3)#

#"take out the common factor " (2x-3)#

#=(2x-3)(color(red)(2x+7))#

#rArr4x^2+8x-21=(2x-3)(2x+7)#

#rArr(2x-3)" and " (2x+7)" are possible dimensions"#

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