factor completely: 2x^2+11x+5?

Factoring gives you: (2x + 1) * (x + 5) = 2x^2 + 11x + 5

I did that in my head, but If you had wanted to use the quadratic formula, a safe but time-consuming technique, you would have gotten:

.......-11 +/ sqrt(121 - 40)
x = ----------------------------- =
.......................4

[-11 +/- sqrt(81)] / 4

(- 11 +/- 9) / 4 = -5 and -1/2

So the answer is 2 * (x + 5) * (x + (1/2))

Check: 2 * (x + (1/2)) = 2x + 1

(2x + 1) * (x + 5) = 2x^2 + 11x + 5

(2x + 1) * (x + 5).....<<<<<...Answer
.

2x² + 11x + 5 = 0
x² + 11/2x = - 5/2
x² + 11/4x = - 5/2 + (11/4)²
x² + 11/4x = - 40/16 + 121/16
(x + 11/4)² = 81/16
x + 11/4 = 9/4

= x + 11/4 - 9/4, = x + 2/4, = x + 1/2, = 2x + 1
= x + 11/4 + 9/4, = x + 20/4, = x + 5

Answer: (2x + 1)(x + 5) are the factors.

(2x+1)(x+5)
x = -1/2, x = -5

( 2x + 1 ) ( x + 5 )

2x^2 + 11x + 5
= 2x^2 + 10x + x + 5
= (2x^2 + 10x) + (x + 5)
= 2x(x + 5) + 1(x + 5)
= (x + 5)(2x + 1)

(2x + 1)(x +5)

This is (2x+1)(x+5). You can check to see my answer is correct by using the FOIL method. Check out my Math Variety blog post on this topic and click on ads/links of interest:
http://mathvariety.blogspot.com/2009/04/foil-method.html

Here's the process.

You want (ax+b)(cx+d) = 2x^2 + 11x + 5
(let's call "(ax+b)(cx+d)" a "general form")
Multiplying out the left side you get
acx^2 + (ad + bc)x + bd = 2x^2 + 11x + 5

So ac = 2
(ad + bc) = 11
and
bd = 5

(A) Ok, when you're just learning, usually problems, if they're factorable, factor into integers.
So,
(B) For ac = 2, either a=1 and b=2 or a=2 and b=1. So you have
(x+b)(2x+d) = 2x^2 + (d + 2b)x + bd = 2x^2 + 11x + 5

(C) Now, looking at bd=5,
b=1 and d=5, or b=5 and d=1

(D) We could just try them both and see which works, but let's look at
d+2b = 11, keeping in mind our possible factors from above (C)
(1) + (2)(5) = 11
That makes d=1 and b=5

Substituting into our "general form"
(x+5)(2x+1)
And, if you multiply that out, you do get 2x^2 + 11x +5... so it checks.

Here's a footnote. Applying the Quadratic Formula is NOT factoring. It's used when things don't factor easily.
Also, the way those who "did it in their head" is outlined above. The way to "check" is to multiply out the factors... as I showed... not to check it against the quadratic formula.

2x^2+11x+ 5
2x^2+ x + 10x + 5
x(2x + 1) + 5(2x + 1)
(x+5), (2x+1) are the factors

It's a quadratic so it has at most two factors.

the first coefficient has 2 and 1 as the only factors, so the factorization must begin like this:

(2x + ?) (x + ?)

The last coefficient has 5 and 1 as the only factors, so the only possibilities that match the first and third coefficients are

(2x + 5) (x + 1) OR (2x + 1) (x + 5)

But we have to get a middle coefficient of 11. The second expression has that, so it is the factorization.