need to factor?

Question

7z^2 - 23z + 16

Answer 1

Let me show you something called the AC method.

Take the A coefficient times the C and get 7*16 = 112.

Now, list the factor pairs of 112 until you find two numbers that add to give -23. Since the product is positive and the sum is negative, we know to only try the negative numbers.

-1, -112
-2, -56
-4, -28
-7, -16 Done here
-8, -14

Now, split the middle number into -7 and -16 like this

7x^2 -7x -16x +16 and factor by parts.

7x(x-1) -16(x-1) and now factor out the (x-1)
(7x - 16)(x - 1)

Answer 2

Ok, since 7 is prime we know the factors are 7 and 1, and since 16 is not, it factors to 1*16, 2*8, or 4*4

As it turns out:

(7z - 16)(z-1) gives us the result we want because if we FOIL (first, outside, inside, last) we get:

F: 7z * z
O: 7z * -1
I: -16 * z
L: -16 * -1

7z^2 -7z -16z + 16 = 7z^2 -23z +16

Hope this helps!

Answer 3

7z^2 - 23z + 16
(7x-16)(x-1)

Answer 4

7z² = 23z + 16

(7x - 16)(z - 1) = 7x² - 16x - 7z + 16 = 7z² - 23z + 16

The answer is (7z - 16)(z - 1)

- - - - - - - -s-

Answer 5

(z- 1)(7z-16)

which you could also say z equals both 1 and 2.286
God Bless!

Answer 6

(7z-16)(z-1)

Answer 7

See also the factoring lesson at the link below.

Answer 8

(3z - 12)(4z + 4)