algebra Help Please?

Question

factor the polynomial if factoring is possible, please show me the steps so I can understand this better thanks
x^2 + 17x +16

Answer 1

X^2 + 17X + 16

X^2 + X + 16X +16
X(X+1) + 16(X+1)
(X+1)(X+16)

Answer 2

I did the ABC method where you take the middle term (B) and then multiply the outer terms (A and C) and whatever you add up to B must also multiply together to get A and C...such as you have 17. 1+16 = 17, which also means 1 times 16 is 16...then you take those terms and put them back into the equation so you get:

x^2+x+16x+16 (notice how the middle terms can be added to get 17x).

then factor them out like:

x(x+1)+16(x+1), the (x+1) must always be the same in each part in any problem...it can be something different but each time they must be the same).

You just take one of the (x+1)s and use the (x+16), so you get:

(x+1)(x+16)

You could have also have done the quadratic formula and gotten the answers, then used their opposite signs:

-b+/- the square root of b^2-4(a)(c) all over 2(a)

so:

-17+/- the square root of 17^2-4(1)(16) all over 2(1)

which gets you:

-17+/- 15 all over 2

then use both signs to come up with the answer:

-17+15 divided by 2, and -17-15 divided by 2....

-1 and -16, take the opposite signs and you get 1 and 16, put them as your factored pairs:

(x+1)(x+16)

There are a few other ways, but hopefully you understand those parts!

Answer 3

Try to think of two numbers that multiply to 16 and add to 17. This is really easy, the number will be 16 and 1: 16 times 1 is 16, 16 plus 1 is 17.

The factored result would be:
(x + 16)(x + 1)

Answer 4

x^2 + 17x +16

It will be of the form (x+_)(x+_). Ask yourself, what two factors of 16 will add to 17? The answer in this case is 16 and 1 ( 16*1 = 16 ; 16 + 1 = 17).

So the answer is:

x^2 + 17x +16 = (x+16)(x+1)

Answer 5

x^2 + 17 x + 16

Find the factors of positive 16 that add up to positive 17

Those would be 16 and 1

So the factored version would be (x +1)(x+16)

To check your work FOIL the factors back out.

F = x^2
O = 16x
I = x
L = 16

x^2 + 16x + x + 16 or x^2 + 17x + 16

Answer 6

to get x^2 you must first have to x's
(x ) (x )
It is a positive number so you need two positive signs
(x+ ) (x+ )
what adds to get 17 and multiplies to get 16?
16 and 1
(x+1) (x+16
check using foil
x*x=x^2
1*x=1x
16*x=16x
1*16=16x
x^2+1x+16x+16
Simplify
x^2+17x=16
:)