How do you factor the expression #2x^2 + 21x + 49#?

1 Answer
George C.
May 1, 2016

#2x^2+21x+49=(2x+7)(x+7)#

Explanation:

Use an AC method. Find a pair of factors of #AC=2*49=98# with sum #B=21#.

There are not many ways to split #98 = 2*7*7# into a product of two factors, so we can quickly find: #14*7 = 98# and #14+7=21#.

Use this pair to split the middle term and factor by grouping:

#2x^2+21x+49#

#=2x^2+14x+7x+49#

#=(2x^2+14x)+(7x+49)#

#=2x(x+7)+7(x+7)#

#=(2x+7)(x+7)#

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