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

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Answer 1 · 2016-05-01T14:20:17

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

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:

$2x^2+21x+49$

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

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

$=2x(x+7)+7(x+7)$

$=(2x+7)(x+7)$

How do you factor the expression 2x^2 + 21x + 492x^2 + 21x + 49?