Question

factor 5x^2+22x+17

Answer 1

notice 5 and 17 are both prime and add to 22
(5x+17)(x+1)

Answer 2

Here's how I'd go about it:

the coefficient in front of x^2 is 5. The only two integers that multiply to five are 1 and 5. That means the factored form will look like this:

(5x +/- ?)(x +/- ? )

Since the constant term is 17, and the only two numbers that multiply to 17 are 1 and 17, that means the factored form will look like this:

(5x +/- 1)(x +/- 17)
or
(5x +/- 17)(x +/- 1)

Since the coefficient of x is 22, and 22 just happens to be 17 + 5, the factored form looks like this:

(5x+17)(x+1)

Check it to make sure! :)

Answer 3

5x^2+22x+17
5x^2+5x+17x+17
5x(x+1)+17(x+1)
(x+1)(5x+17)