How do you factor #x^2 + 7x + 8x + 56# by grouping?

Question

Eli Assouline · Accepted Answer

#x=-8# & #x=-7#

Let's look at the #x^2+7x# and the #8x+56# separately.

#color(red)(x^2+7x)+color(blue)(8x+56)=0#

We can factor an #x# out of the red term, and an #8# out of the blue term. We get:

#color(red)(x(x+7))+color(blue)(8(x+7))=0#

Since #x+7# is multiplying two terms, we can rewrite this as:

#(x+8)(x+7)=0#

Setting the factors equal to zero, we get:

#x=-8# & #x=-7#

Ethan Adkins · Answer

#(x+8)(x+7)# This expression is already in the perfect form for grouping. Note that #x^2+7x = x(x+7)# and #8x+56 = 8(x+7)# so that both pairs of terms in #color(red)(x^2+7x)+color(blue)(8x+56)# have a common factor : #color(red)(x^2+7x)+color(blue)(8x+56) = color(red)(x(x+7))+color(blue)(8(x+7)) # You can now use the law #bcolor (red)a+c color(red)a = (b+c)color(red)a# to write this as #(x+8)(x+7)#

Nathan Axel · Answer

undefined To factor $x^2 + 7x + 8x + 56$ by grouping, first, group the terms in pairs:

$x^2 + 7x$ and $8x + 56$

Then, factor out the greatest common factor from each pair:

$x(x + 7)$ and $8(x + 7)$

Now, we can see that both terms have a common factor of $(x + 7)$. Factor out this common factor:

$(x + 7)(x + 8)$

Therefore, the factored form of $x^2 + 7x + 8x + 56$ is $(x + 7)(x + 8)$.