What is the coefficient of the x-term of the factorization of 25x^2+20x+4

Answer 1

To factor 25x^2 + 20x +4, the only way to factor 25 into integers is either 25 and 1 or 5 and 5. If it is factored as 5 and 5, you can then factor the last term, 4, into 2 and 2, to get the factorization of

25x^2 + 20x + 4 = (5x+2)*(5x+2)

Answer 2

Payton,

The quickest way to see the answer is using the substitution method:

If we make u = 5x, Why like that?

Well if u = 5x

then u² = (5x)(5x) = 25x²

and 4u = (4)(5x) = 20x

So plug those into the equation and now it goes from:

Before: 25x²+20x+4

After: u² +4u+ 4

Now we can easily see get the factors for this equation!

It is (u +2)(u+2) or in the simplest form (u+2)²

But, we need our answer in terms of x, so we replace the 5x for every u we see in the answer:

So (u+2)²

Becomes -> (5x+2)²

There is only one coefficient on the x term and that is 5!

Try multiplying it back out to verify that the equations are indeed the same. They are! Good luck with Algebra!

Answer 3

25x² + 20x + 4

(5x + 2)²