Answer:
(4x + 10)(x + 7)
Step-by-step explanation:
I have to tell you how very well you have expressed the question. We don't often get things so carefully done.
This is not an easy question. What makes it hard is the 4 and you can't do anything to get rid of it like use the distributive property. However there is one thing that is coming to the rescue and that is the 70. It doesn't have very many prime factors and one of them has to be a 7. It must be present in some form or another. You have one more thing going for you. Everything is plus. So here's what you know so far.
( x + something)(4x in some form + 7) or
(2x + something)(2x + 7 ) or
(4x + something)(x + 7)
One of those three must be correct
<em><u>Try the first one first</u></em>
(x + 10)(4x + 7) when you expand it you get
(4x^2 + 40x + 7x + 70) which makes the middle term 47x not 38x so this answer is not correct.
<em><u>Middle attempt</u></em>
(2x + 10)(2x + 7) We could take out the common factor of 2.
4x^2 + 20x + 14x + 70 = 4x^2 + 34x + 70
<em><u>Last chance</u></em>
(4x + 10)(x + 7) Foil this.
4x^2 + 28x + 10x + 70
4x^2 + 38x + 70
