Question

Factor by grouping (sometimes called the ac-method). 8x^2+22x+5

First, choose a form with appropriate signs.
Then, fill in the blanks with numbers to be used for grouping.
Finally, show the factorization.

Answer 1

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We can factor 8x^2+22x+5 by grouping.

First, we need to find two numbers whose product is 8*5=40 and whose sum is 22. These numbers are 2 and 20.

Next, we rewrite the middle term 22x as 2x+20x.

8x^2 + 2x + 20x + 5

Now we group the first two terms and the last two terms together.

2x(4x+1) + 5(4x+1)

We can see that both terms have a common factor of (4x+1), so we can factor it out.

(2x+5)(4x+1)

Therefore, the factorization of 8x^2+22x+5 is (2x+5)(4x+1).