Algebra help please Anyone ?

Question

I need to factor x^2 + 17x + 16I do not know how to do this and I need to show each step of factoring out the GCF before I go to the next step, can anyone please help with this I am so lost on this
Thanks a great deal

Answer 1

x² + 17x + 16 = 0

x² + x + 16x + 16 = 0

x(x + 1) + 16(x + 1) = 0

(x + 16)(x + 1) = 0

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Answer 2

Well a really nice method that works with Quadratic equations of the form ax^2 + bx + c = 0, when the coefficient of x^2 is one like in your problem you simply do this:


x^2 + 17x + 16. multiplying the first term by the last term 1X16 = 16, so you need two number which multiply to give 16 and add up to give the middle number which is 17.

These two are quite easily 16 and 1 because 16X1=16 and 16 + 1 = 17 - so the answer is = (X+16)(X+1)

If you want the possible values of X you put your answer = 0, like so:

(X+16)(X+1) = 0

Now logically if the answer is zero, when one of these terms HAS TO BE ZERO.

so you do them seperately:

Either X+16 = 0 or X + 1 = 0

Hence X = -16 or X=-1.
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If you plug these values that you have found back into the equation you'll see that it all adds up to zero, hence the equation is satisfied.

If you expand (X+16)(X+1) you end up with what you started with - which is the whole point.

Hope this helps!

Answer 3

x^2 + 17x + 16 .............(1)
As all the terms are positive, and the coefficient of x^2 is 1, the factors are going to be of the form:
(x + a)(x + b).
If you multiply this out, you get:
x^2 + (a + b)x + ab ........(2)

Comparing coefficients of (1) and (2):
a + b = 17
ab = 16
The possibilities for ab = 16 are:
16:1 or 8:2 or 4:4
Out of those, only 16:1 are going to make a + b = 17.
From (2) therefore, the factors are:
(x + 16)(x + 1).

Answer 4

Factors of 16: 1,2,4,8,16

1 + 16 = 17

x^2 + 17x + 16

x^2 + 1x + 16x + 16

x(x+1) + 16(x+1)

(x+16)(x+1)

Answer 5

Call the factors (x+a) and (x+b), where a and b are what you want to find out.

The product of the two factors is x^2 + (a+b)x + ab.

Compare this with your quadratic form. You need a and b to satisfy:

a+b = 17
ab = 16

In other words, you need to find two factors of 16 that add up to 17. It's not too hard (by trial and error) to discover that they are 1 and 16.

Answer 6

x^2 + 17x + 16

Factors of 16 are-: [1,16] or [2,8] or [4,4]

In this case we need the products to add up to 17, as this is the middle term.....therefore we pick 1 and 16 as our factors.

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

Answer 7

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

Answer 8

16 = 1X16
16=2X8
16=4X4

Those are the factors of the constant. If you know how to use this information, it should help with your next step.

Answer 9

x^2 + 17x +16
=(x+16)(x+1) ie = x^2 +16x+1x+17
therefore x=-16 or x=-1

Answer 10

Y=Mx+b