Question 250595: factoring completely
16x^2 + 24x + 9
Found 2 solutions by edjones, PRMath:
Answer by edjones(8007)   (Show Source):
You can put this solution on YOUR website! 16x^2 + 24x + 9
16*9=144 the 2 factors of 144 whose sum is 24 are 12 & 12.
16x^2+12x+12x+9
=4x(4x+3)+3(4x+3) factor by grouping.
=(4x+3)^2
.
Ed
Answer by PRMath(133)  (Show Source):
You can put this solution on YOUR website! 
To factor this, you sort of do a "reverse" of FOIL. You know that FOIL stands for First, Outside, Inside, Last.
Usually with FOIL, we start with two sets of parenthesis:
We want the first term in each set of parenthesis to multiply together to reach  .
So, let's think of a fairly typical way that you can reach 16 when you multiply two numbers together. How about the number 4?
4 times 4 = 16 yes? We cannot forget there is an  term there, so let's put in that x times x = .
We now have:
(4X ________)(4X ________)
Now in the equation you gave: we have to come up with a way that will let us MULTIPLY two numbers to reach 9 and yet ADD together to reach 24.
A pretty typical way to reach 9 thru multiplication of two numbers is to use 3 times 3.
So, now we have:
(4X ????? 3)(4x ????? 3).
What do we do with the 3? Is it positive or negative? Well the 9 in the equation is positive, as is the 24, so let's try a positive 3.......
(4x + 3)(4x + 3)
Does this give us our original equation of: ?
Let's check:
FOIL:
First terms: 4x times 4x =
Outside terms: 4x times 3 = 12x
Inside terms: 4x times 3 = 12x
Last terms: 3 times 3 = 9
That means we have: + 12x + 12x + 9
Let's combine like terms of 12x + 12x = 24X and rewrite what we have: + 24x + 9
Ok! That's our original equation. Therefore, (4x + 3)(4x + 3)
(or you can write it as:  ) is a way to factor: + 24x = 9
I hope this helps. :-)
|
|
|
