Question

The area of a rectangular garden is 2g² + 34g + 140. If the width is 2g + 14 what is the length?

Please answer I need it for a homework problem

Answer 1

(2g² +34g +140) = (2g +14)*(g +10) 

Answer 2

You can use synthetic division to find the other factor, or you can simply divide the leading and trailing terms by the numbers you have. (This works if the binomial you have is truly a factor of the trinomial, which it is.)

2g²/2g = g
140/14 = 10
Your other factor (the length) is g+10.

(2g² +34g +140) = (2g +14)*(g +10)