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

Question

Nathan Axel · Accepted Answer

#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)#

Jace Anderson · Answer

undefined To factor the expression $2x^2 + 21x + 49$, you can use the quadratic formula or factor by grouping. Factoring by grouping involves splitting the middle term into two terms such that when you group them, you can factor out a common factor.

First, find two numbers that multiply to $2 \times 49 = 98$ and add to $21$. These numbers are $14$ and $7$.

Now, rewrite the middle term $21x$ as $14x + 7x$.

Next, factor by grouping:

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

Factor the first two terms by taking out the common factor $2x$:

$2x(x + 7)$

Factor the last two terms by taking out the common factor $7$:

$7(x + 7)$

Now, notice that both $x + 7$ terms are the same. Factor out $x + 7$:

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

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

Therefore, the factored form of $2x^2 + 21x + 49$ is $(2x + 7)(x + 7)$.