Help please?

Question

Factor completely:


x^2 + 17x + 16

how do I solve this step by step.. Doing some practice problems to get a hang of it

Answer 1

(x+16)(x+1)
since there are only positve numbers, the factored equation will also be with plus signs.
First find what numbers can be multiplied to equal 16
4*4 or 1*16 or 8*2
Now you have to see which of those sets of numbers can be added to equal 17
so you use 1 and 16 because they add to 17 **

Answer 2

I will try to help in this.

First, you need to find out what is the value if you multiply 16 and 1. (Because we have one x^2. if you have 2x^2, you will take 2 X 16).
16 is the answer. Now, find out the factors of 16, so that the sum of them is 17.
The answer is 16 and 1. (If we multiply, we will get 16 and if we add, we will get 17.)

Now, write the same equation like this :
x^2 + x + 16x + 16 ( remember x + 16x = 17x)

now, take x common from the first two and 16 common from the next two. It will become :
x(x+1) + 16(x+1)

Now, take (x+1) common from the above. It will become :

(x+1)(x+16)
These are the factors.

Sorry if I've confused you.

Answer 3

this is a classic second order polynominal of the form:

AX^2 + BX + C

in the equation above, A=1, B=17 and C=16. The two "roots" of the equation are given by:

(-B +/- SQRT(B^2 -4AC))/2A

and thus x = (-17 + SQRT(17*17 - 4*1*16))/2*1
and thus x = (-17 - SQRT(17*17 - 4*1*16))/2*1

BTW: the answer is what x has to be so that the equation equals zero. Also, if the result of what's inside the SQRT() function is less than zero, there is no solution to the problem.

Answer 4

(x+16)(x+1) since 16*1=16 and 16+1=17

Answer 5

x^2 + 17x + 16=(x+1)(x+16)
b/c 16=1x16
=2x8
=4x4
sum of 17=1+16
you can double check:
(x+1)(x+16)=x^2+16x+1x+16
=x^2+17x+16

Answer 6

x^2 + 17x + 16 = x^2 + 2*8.5*X + 8.5^2 - 8.5^2 + 16 =
= (x + 8.5)^2 - 72.25 + 16 = (x + 8.5)^2 - 56.25 =
= (x + 8.5)^2 - 7.5^2 = (x + 8.5 - 7.5)(x + 8.5 + 7.5) =
= (x + 1)(x + 16)

Or if you've noticed that 17=16 + 1, and 16 = 16*1:
x^2 + 17x + 16 = x^2 + 16x + x + 16 = x(x + 16) + 1(x + 16) =
= (x + 1)(x + 16)

Answer 7

(x + 16)(x + 1)

In this case, it's easy. What two numbers, when added together give you 17, and when multiplied together give you 16? The answer is 1 and 16.

Answer 8

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