How do you factor the expression #3x^2+ 10x + 7#?

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Answer 1 · 2018-07-27T09:27:59

#(x+1)(3x+7)#

Given quadratic polynomial:

#3x^2+10x+7#

#=3x^2+3x+7x+7#

#=3x(x+1)+7(x+1)#

#=(x+1)(3x+7)#

Answer 2 · 2018-07-27T09:32:30

#p(x)=(x+1)(3x+7)#

Let ,

#p(x)=3x^2+color(red)(10x)+7#

Here ,

#color(blue)(3 xx7=21 and 3+7=10#

#:.p(x)=ul(3x^2+color(red)(3x))+ul(color(red)(7x)+7)#

#:.p(x)=3x(x+1)+7(x+1)#

#:.p(x)=(x+1)(3x+7)#

Answer 3 · 2018-07-28T00:34:53

#(3x+7)(x+1)#

We can use the strategy factoring by grouping. Here, we can split up the #b# term so we can factor the left and right sides.

Here's what I mean. We can rewrite this as

#color(steelblue)(3x^2+3x)+color(purple)(7x+7)#

Out of the blue term, we can factor out a #3x#, and the purple term, we can factor out a #7#. This leaves us with:

#color(steelblue)(3x(x+1))+color(purple)(7(x+1))#

Since both terms have an #x+1# in common, we can factor that out to get

#(3x+7)(x+1)#

Hope this helps!